Search

It is a well-studied phenomenon in AdS$_3$/CFT$_2$ that pure states often appear 'too thermal' in the classical gravity limit, leading to a version of the information puzzle. One example is the case of a heavy scalar primary state, whose associated classical geometry is the BTZ black hole. Another example is provided by a heavy left-moving primary, which displays late time decay in chiral correlators. In this paper we study a special class of pure state geometries which do not display such information loss. They describe heavy CFT states created by a collection of chiral operators at various positions on the complex plane. In the bulk, these take the form of multi-centered solutions from the backreaction of a collection of spinning particles, which we construct for circular distributions of particles. We compute the two-point function of probe operators in these backgrounds and show that information is retrieved. We observe that the states for which our geometric picture is reliable are highly extended star-like objects in the bulk description. This may point to limitations of the semiclassical fuzzball picture of black hole microstates., Comment: 48 pages, 12 figures, published version

In according with the stated conception the purpose of the present work is the reconstruction of some of innumerable microstates of α phase of ferritic steels, definition of its macroparameters and their subsequent comparison with indicators of mechanical properties of industrially let out steels. The establishment of a correlation between the measured indicators of mechanical properties of already created materials and the calculated state parameters of their basic phase opens an opportunity of mechanical properties prediction of materials in dependence on their prehistory that as a matter of fact represents the central task of material science. Simulation of α-phase state of series of industrially let out ferritic steels and alloys is executed in the assumption of identity of its composition to composition of steel or alloy as a whole. The correlation between indicators of mechanical properties of steels and alloys and state parameters of their basic phase is traced.

Nonequilibrium thermodynamics as applied to polymeric liquids is limited by the inability to quantify the configurational entropy. There is no known experimental method to determine it rigorously. Theoretically, entropy is based entirely on the configurational microstate of the material, but for polymer liquids, the number of available configurations is immense and covers long length scales associated with the chain-like nature of the constituent molecules. In principle, however, it should be possible to calculate the entropy from a realistic molecular dynamics simulation that contains positional data for each atomic unit making up the polymer macromolecules. However, there are two challenges in calculating the entropy from an atomistic simulation: it is necessary to relate atomic positions to configurational mesostates, depending on the degree of coarse-graining assumed (if any), and then to entropy, and considerable computational resources are required to determine the three-dimensional probability distribution functions of the configurational mesostates. In this study, a method was developed to calculate nonequilibrium entropy using 3d probability distributions for a linear, entangled polyethylene melt undergoing steady-state shear and elongational flow. An approximate equation expressed in terms of second moments of the 3d distributions was also examined, which turned out to provide almost identical values of entropy as the fully 3d distributions at the mesoscopic level associated with the end-to-end vector of the polymer chains.

During the physical foundation of his radiation formula in his December 1900 talk and subsequent 1901 article, Planck refers to Boltzmann’s 1877 combinatorial-probabilistic treatment and obtains his quantum distribution function, while Boltzmann did not. For this, Boltzmann’s memoirs are usually ascribed to classical statistical mechanics. Agreeing with Bach, it is shown that Boltzmann’s 1868 and 1877 calculations can lead to a Planckian distribution function, where those of 1868 are even closer to Planck than that of 1877. Boltzmann’s and Planck’s calculations are compared based on Bach’s three-level scheme ‘configuration–occupation–occupancy’. Special attention is paid to the concepts of interchangeability and the indistinguishability of particles and states. In contrast to Bach, the level of exposition is most elementary. I hope to make Boltzmann’s work better known in English and to remove misunderstandings in the literature.

Multi-centered bubbling solutions are black hole microstate geometries that arise as smooth solutions of 5-dimensional $\mathcal{N}=2$ Supergravity. When these solutions reach the scaling limit, their resulting geometries develop an infinitely deep throat and look arbitrarily close to a black hole geometry. We depict a connection between the scaling limit in the moduli space of Microstate Geometries and the Swampland Distance Conjecture. The naive extension of the Distance Conjecture implies that the distance in moduli space between a reference point and a point approaching the scaling limit is set by the proper length of the throat as it approaches the scaling limit. Independently, we also compute a distance in the moduli space of 3-centre solutions, from the K\"ahler structure of its phase space using quiver quantum mechanics. We show that the two computations of the distance in moduli space do not agree and comment on the physical implications of this mismatch., Comment: 29 pages, 2 figures. V2: reference added. V3: revised version accepted for publication in JHEP. V4: Added funding information

The Onsager linear relations between macroscopic flows and thermodynamics forces are derived from the point of view of large deviation theory. For a given set of macroscopic variables, we consider the short-time evolution of near-equilibrium fluctuations, represented as the limit of finite-size conditional expectations. The resulting asymptotic conditional expectation is taken to represent the typical macrostate of the system and is used in place of the usual time-averaged macrostate of traditional approaches. By expanding in the short-time, near-equilibrium limit and equating the large deviation rate function with the thermodynamic entropy, a linear relation is obtained between the time rate of change of the macrostate and the conjugate initial macrostate. A Green-Kubo formula for the Onsager matrix is derived and shown to be positive semi-definite, while the Onsager reciprocity relations readily follow from time reversal invariance. Although the initial tendency of a macroscopic variable is to evolve towards equilibrium, we find that this evolution need not be monotonic. The example of an ideal Knundsen gas is considered as an illustration., 25 pages, 3 figures

Two-dimensional CFTs have an infinite set of commuting conserved charges, known as the quantum KdV charges. We study the Generalized Gibbs Ensemble with chemical potentials for these charges at high temperature. In a large central charge limit, the partition function can be computed in a saddle-point approximation. We compare the ensemble values of the KdV charges to the values in a microstate, and find that they match irrespective of the values of the chemical potentials. We study the partition function at finite central charge perturbatively in the chemical potentials, and find that this degeneracy is broken. We also study the statistics of the KdV charges at high level within a Virasoro representation, and find that they are sharply peaked., Comment: 19 pages, no figures; v2: references added & updated

A system in equilibrium does not evolve -- time independence is its telltale characteristic. However, in Newtonian physics the microstate of an individual system (a point in its phase space) evolves incessantly in accord with its equations of motion. Ensembles were introduced in XIX century to bridge that chasm between continuous motion of phase space points in Newtonian dynamics and stasis of thermodynamics: While states of individual classical systems inevitably evolve, a phase space distribution of such states -- an ensemble -- can be time-independent. I show that entanglement (e.g., with the environment) can yield a time-independent equilibrium in an individual quantum system. This allows one to eliminate ensembles -- an awkward stratagem introduced to reconcile thermodynamics with Newtonian mechanics -- and use an individual system interacting and therefore entangled with its heat bath to represent equilibrium and to elucidate the role of information and measurements in physics. Thus, in our quantum Universe one can practice statistical physics without ensembles -- hence, in a sense, without statistics. The elimination of ensembles uses ideas that led to the recent derivation of Born's rule from the symmetries of entanglement, and I start with a review of that derivation. I then review and discuss difficulties related to the reliance on ensembles and illustrate the need for ensembles with the classical Szilard's engine. A similar quantum engine -- a single system interacting with the thermal heat bath environment -- is enough to establish thermodynamics. The role of Maxwell's demon (which in this quantum context resembles Wigner's friend) is also discussed., to appear in Physics Reports

If the evaporation of a black hole formed from a pure state is unitary, the entanglement entropy of the Hawking radiation should follow the Page curve, increasing from zero until near the halfway point of the evaporation, and then decreasing back to zero. The general argument for the Page curve is based on the assumption that the quantum state of the black hole plus radiation during the evaporation process is typical. In this paper, we show that the Page curve can result from a simple dynamical input in the evolution of the black hole, based on a recently proposed signature of quantum chaos, without resorting to typicality. Our argument is based on what we refer to as the "operator gas" approach, which allows one to understand the evolution of the microstate of the black hole from generic features of the Heisenberg evolution of operators. One key feature which leads to the Page curve is the possibility of dynamical processes where operators in the "gas" can "jump" outside the black hole, which we refer to as void formation processes. Such processes are initially exponentially suppressed, but dominate after a certain time scale, which can be used as a dynamical definition of the Page time. In the Hayden-Preskill protocol for young and old black holes, we show that void formation is also responsible for the transfer of information from the black hole to the radiation. We conjecture that void formation may provide a microscopic explanation for the recent semi-classical prescription of including islands in the calculation of the entanglement entropy of the radiation., 48 pages, 15 figures

This chapter discusses the nature of microscopic configurations and states for systems of particles, accessibility of microscopic states, introduces the Fundamental Postulate of statistical mechanics and illustrates it explicitly for small model systems. The ensemble concept is applied to an isolated system of two subsystems, one small (but still macroscopic), the other much larger (the reservoir). A canonical ensemble describes a small system that can exchange energy, but not matter, with the reservoir, while a grand ensemble describes a small system that can exchange both energy and matter with the reservoir. The canonical partition function that determines the probability for the particle to be in a specific energy state is obtained for a single-particle that can access various types of energy, and is then generalized to many particles and to mixtures. The grand partition function is similarly developed for a system that can exchange both energy and matter with the reservoir.

We compute the Bekenstein-Hawking entropy of near-extremal asymptotically AdS$_4$ electrically charged rotating black holes using three different methods: (i) from the gravity solution, (ii) from the near-horizon Kerr/CFT correspondence and (iii) from the boundary conformal field theory. The results from these three different approaches match exactly, giving us a unique and universal expression for the entropy and the microstate counting of near-extremal AdS black holes via the AdS/CFT correspondence. In the second method, we extend the Kerr/CFT correspondence to the near-extremal case to compute the left and right central charges. We also use hidden conformal symmetry of the near-horizon geometry to compute the Frolov-Thorne temperatures. From the results of the near-extremal AdS$_4$ black hole entropy, we provide a microscopic foundation for Hawking radiation., 25 pages, 2 figures; v2: Sec. 2.1 and Sec. 2.3 updated; v3: published version in JHEP, minor changes in Sec. 2 and 3

We present a first-principles thermodynamic approach to provide an alternative to the Langevin equation by identifying the deterministic (no stochastic component) microforce F_{k,BP} acting on a nonequilibrium Brownian particle (BP) in its kth microstate m_{k}. (The prefix micro refers to microstate quantities and carry a suffix k.) The deterministic new equation is easier to solve using basic calculus. Being oblivious to the second law, F_{k,BP} does not always oppose motion but viscous dissipation emerges upon ensemble averaging. The equipartition theorem is always satisfied. We reproduce well-known results of the BP in equilibrium. We explain how the microforce is obtained directly from the mutual potential energy of interaction beween the BP and the medium after we average it over the medium so we only have to consider the particles in the BP. Our approach goes beyond the phenomenological and equilibrium approach of Langevin and unifies nonequilibrium viscous dissipation from mesoscopic to macroscopic scales and provides new insight into Brownian motion beyond Langevin's and Einstein's formulation., 16 pages; 2 figures; some overlap with arXiv:1901.11192

The “embedded cluster reference interaction site model” (EC-RISM) integral equation theory is applied to the problem of predicting aqueous pKa values for drug-like molecules based on an ensemble of tautomers. EC-RISM is based on self-consistent calculations of a solute’s electronic structure and the distribution function of surrounding water. Following-up on the workflow developed after the SAMPL5 challenge on cyclohexane-water distribution coefficients we extended and improved the methodology by taking into account exact electrostatic solute–solvent interactions taken from the wave function in solution. As before, the model is calibrated against Gibbs energies of hydration from the “Minnesota Solvation Database” and a public dataset of acidity constants of organic acids and bases by adjusting in total 4 parameters, among which only 3 are relevant for predicting pKa values. While the best-performing training model yields a root-mean-square error (RMSE) of 1 pK unit, the corresponding test set prediction on the full SAMPL6 dataset of macroscopic pKa values using the same level of theory exhibits slightly larger error (1.7 pK units) than the best test set model submitted (1.7 pK units for corresponding training set vs. test set performance of 1.6). Post-submission analysis revealed a number of physical optimization options regarding the numerical treatment of electrostatic interactions and conformational sampling. While the experimental test set data revealed after submission was not used for reparametrizing the methodology, the best physically optimized models consequentially result in RMSEs of 1.5 if only improved electrostatic interactions are considered and of 1.1 if, in addition, conformational sampling accounts for quantum-chemically derived rankings. We conclude that these numbers are probably near the ultimate accuracy achievable with the simple 3-parameter model using a single or the two best-ranking conformations per tautomer or microstate. Finally, relations of the present macrostate approach to microstate pKa results are discussed and some illustrative results for microstate populations are presented.

We compute energy gaps and study infalling massive geodesic probes in the new families of scaling, microstate geometries that have been constructed recently and for which the holographic duals are known. We find that in the deepest geometries, which have the lowest energy gaps, the geodesic deviation shows that the stress reaches the Planck scale long before the probe reaches the cap of the geometry. Such probes must therefore undergo a stringy transition as they fall into microstate geometry. We discuss the scales associated with this transition and comment on the implications for scrambling in microstate geometries., Comment: 22 pages, 1 figure

Energy and entropy are competitors in thermodynamics, as an increase in one usually leads to a decrease in the other. In this article, we show that competition between potential energy and entropy also exists in contact problems, which is revealed in the process of solving contact forces in the finite element model of elastic contact problems based on the principle of minimum potential energy and the principle of maximum entropy. First, we discretize the contact problem with finite elements and model it as a quadratic programming problem with the potential energy as the objective and non-penetration conditions as the constraints. Second, by normalizing the Lagrange multipliers—the potential nodal contact forces—in the Lagrangian duality, we obtain an explicit formulation of the displacements as expressed by the normalized potential nodal contact forces. Third, analogous to the concepts in statistical physics, we consider each normalized potential nodal contact force as the probability of the node occupying a microstate, and with the maximum entropy principle, we obtain an explicit formulation of the normalized potential nodal contact forces as expressed by the displacements. Fourth, we construct an iterative procedure for solving the contact forces based on the previous two formulations. The initial value of each normalized nodal contact force, which is one divided by the number of potential contact nodes, is used to calculate the displacements in the first iteration, the iterations continue until a termination condition that is based on the monotonicity of the potential energy is met. Finally, we provide some examples to verify the iterative algorithm and the competition between the potential energy and entropy in the iterative procedure, which takes the form of a decrease in entropy and an increase in potential energy.

In this work, we use quantum complexity theory to quantify the difficulty of distinguishing eigenstates obeying the Eigenstate Thermalization Hypothesis (ETH). After identifying simple operators with an algebra of low-energy observables and tracing out the complementary high-energy Hilbert space, the ETH leads to an exponential suppression of trace distance between the coarse-grained eigenstates. Conversely, we show that an exponential hardness of distinguishing between states implies ETH-like matrix elements. The BBBV lower bound on the query complexity of Grover search then translates directly into a complexity-theoretic statement lower bounding the hardness of distinguishing these reduced states., 19 pages, 4 figures; minor changes

Traditional electronics employs charge currents to control and transmit information and therefore suffer from energy dissipation due to electron scattering. In the past decade, spin waves (magnons) have been discussed as a more efficient alternative. An important aspect of computing based on magnons is the resonant dynamics' reconfigurability. From this end, nanomagnonics with artificial spin ice offers a wealth of possibilities to control the dynamics. This perspective article reviews experimental and theoretical works on the resonant excitations in the GHz frequency range in artificial spin ice, promising for realizing functional magnonic devices. We discuss both the theoretical formulation and experimental methods to characterize the dynamics in the nanomagnetic arrays. The central part of this perspective is devoted to recent developments targeting full control of the dynamics based on the reprogrammability of the spin-ice microstate with the ultimate goal to realize novel functional devices for logics, computation, and storage concepts based on magnons.

How many structurally different microscopic routes are accessible to a protein molecule while folding? This has been a challenging question to address experimentally as single-molecule studies are constrained by the limited number of observed folding events while ensemble measurements, by definition, report only an average and not the distribution of the quantity under study. Atomistic simulations, on the other hand, are restricted by sampling and the inability to reproduce thermodynamic observables directly. We overcome these bottlenecks in the current work and provide a quantitative description of folding pathway heterogeneity by developing a comprehensive, scalable and yet experimentally consistent approach combining concepts from statistical mechanics, physical kinetics and graph theory. We quantify the folding pathway heterogeneity of five single-domain proteins under two thermodynamic conditions from an analysis of 100 000 folding events generated from a statistical mechanical model incorporating the detailed energetics from more than a million conformational states. The resulting microstate energetics predicts the results of protein engineering experiments, the thermodynamic stabilities of secondary-structure segments from NMR studies, and the end-to-end distance estimates from single-molecule force spectroscopy measurements. We find that a minimum of ∼3-200 microscopic routes, with a diverse ensemble of transition-path structures, are required to account for the total folding flux across the five proteins and the thermodynamic conditions. The partitioning of flux amongst the numerous pathways is shown to be subtly dependent on the experimental conditions that modulate protein stability, topological complexity and the structural resolution at which the folding events are observed. Our predictive methodology thus reveals the presence of rich ensembles of folding mechanisms that are generally invisible in experiments, reconciles the contradictory observations from experiments and simulations and provides an experimentally consistent avenue to quantify folding heterogeneity.

Macrostate and microstate characteristics of interregional nonlinear interdependence of brain dynamics are investigated for Zen-meditation and normal resting EEG. Evaluation of nonlinear interdependence based on nonlinear dynamic theory and phase space reconstruction is employed in the 30-channel electroencephalographic (EEG) signals to characterize the functioning interactions among different local neuronal networks. This paper presents a new scheme for exploring the microstate and macrostate of interregional brain neural network interactivity. Nonlinear interdependence quantified by similarity index is applied to the phase trajectory reconstructed from multi-channel EEG. The microstate similarity-index matrix (miSIM) is evaluated every 5 millisecond. The miSIMs are classified by K-means clustering. The cluster center corresponds to the macrostate SIM (maSIM) evaluated by conventional scheme. Zen-meditation EEG exhibits rather stationary and stronger interconnectivity among frontal midline regional neural oscillators, whereas resting EEG appears to drift away more often from the midline and extend to the inferior brain regions.

We systematically study all supersymmetric solutions of six-dimensional (2,0) supergravity with a null isometry. In particular, every such solution with at least four real supersymmetries is also a supersymmetric solution of a (1,0) theory preserving the same absolute amount of supersymmetry. This implies that no genuinely new solutions of this type can be found in this framework. The microstate geometries associated to supersymmetric black holes within Mathur's proposal are generically supersymmetric solutions of six-dimensional supergravity. A direct consequence of our result is that supersymmetric microstate geometries of single centre supersymmetric black holes should carry only one compact 3-cycle., Comment: 40 pages; v2: minor corrections, version published in General Relativity and Gravitation

In the self-assembly process which drives the formation of cellular membranes, micelles, and capsids, a collection of separated subunits spontaneously binds together to form functional and more ordered structures. In this work, we study the statistical physics of self-assembly in a simpler scenario: the formation of dimers from a system of monomers. The properties of the model allow us to frame the microstate counting as a combinatorial problem whose solution leads to an exact partition function. From the associated equilibrium conditions, we find that such dimer systems come in two types: "search-limited" and "combinatorics-limited", only the former of which has states where partial assembly can be dominated by correct contacts. Using estimates of biophysical quantities in systems of single-stranded DNA dimerization, transcription factor and DNA interactions, and protein-protein interactions, we find that all of these systems appear to be of the search-limited type, i.e., their fully correct dimerization regimes are more limited by the ability of monomers to find one another in the constituent volume than by the combinatorial disadvantage of correct dimers. We derive the parameter requirements for fully correct dimerization and find that rather than the ratio of particle number and volume (number density) being the relevant quantity, it is the product of particle diversity and volume that is constrained. Ultimately, this work contributes to an understanding of self-assembly by using the simple case of a system of dimers to analytically study the combinatorics of assembly., 2nd Version: Correcting typo in Eq. 11; Adding affirmation of Eq. 11 to Supp. Mats.; Updated link to supplementary code

Entropy is an important concept that originated in thermodynamics. It is the subject of the famous Second Law of Thermodynamics, which states that “the entropy of a closed system increases continuously and irrevocably toward a maximum” (Huettner 1976, 102) or “the disorder in the universe always increases” (Framer and Cook 2013, 21). Accordingly, it has been widely regarded as an ideal measure of disorder. Its computation can be theoretically performed according to the Boltzmann equation, which was proposed by the Austrian physicist Ludwig Boltzmann in 1872. In practice, however, the Boltzmann equation involves two problems that are difficult to solve, that is the definition of the macrostate of a system and the determination of the number of possible microstates in the microstate. As noted by the American sociologist Kenneth Bailey, “when the notion of entropy is extended beyond physics, researchers may not be certain how to specify and measure the macrostate/microstate relations” (Bailey 2009, 151). As a result, this entropy (also referred to as Boltzmann entropy and thermodynamic entropy) has remained largely at a conceptual level. In practice, the widely used entropy is actually proposed by the American mathematician, electrical engineer, and cryptographer Claude Elwood Shannon in 1948, hence the term Shannon entropy. Shannon entropy was proposed to quantify the statistical disorder of telegraph messages in the area of communications. The quantification result was interpreted as the information content of a telegraph message, hence also the term information entropy. This entropy has served as the cornerstone of information theory and was introduced to various fields including chemistry, biology, and geography. It has been widely utilized to quantify the information content of geographic data (or spatial data) in either a vector format (i.e., vector data) or a raster format (i.e., raster data). However, only the statistical information of spatial data can be quantified by using Shannon entropy. The spatial information is ignored by Shannon entropy; for example, a grey image and its corresponding error image share the same Shannon entropy. Therefore, considerable efforts have been made to improve the suitability of Shannon entropy for spatial data, and a number of improved Shannon entropies have been put forward. Rather than further improving Shannon entropy, this study introduces a novel strategy, namely shifting back from Shannon entropy to Boltzmann entropy. There are two advantages of employing Boltzmann entropy. First, as previously mentioned, Boltzmann entropy is the ideal, standard measure of disorder or information. It is theoretically capable of quantifying not only the statistical information but also the spatial information of a data set. Second, Boltzmann entropy can serve as the bridge between spatial patterns and thermodynamic interpretations. In this sense, the Boltzmann entropy of spatial data may have wider applications. In this study, Boltzmann entropy is employed to quantify the spatial information of raster data, such as images, raster maps, digital elevation models, landscape mosaics, and landscape gradients. To this end, the macrostate of raster data is defined, and the number of all possible microstates in the macrostate is determined. To demonstrate the usefulness of Boltzmann entropy, it is applied to satellite remote sensing image processing, and a comparison is made between its performance and that of Shannon entropy.

We use spatially resolved magneto-optical Kerr microscopy to track the complete microstates of arrays of perpendicular anisotropy nanomagnets during magnetization hysteresis cycles. These measurements allow us to disentangle the intertwined effects of nearest neighbor interaction, disorder, and stochasticity on magnetization switching. We find that the nearest neighbor correlations depend on both interaction strength and disorder. We also find that although the global characteristics of the hysteretic switching are repeatable, the exact microstate sampled is stochastic with the behavior of individual islands varying between nonminally identical runs.

OBJECTIVE Tracking the spatiotemporal fast (~100 ms) transient networks remains challenging due to a limited understanding of neural activity dynamics as well as a lack of relevant sophisticated methodologies. In this study, we introduce a novel approach to identify simultaneously distinct EEG microstates and their corresponding microstate functional connectivity (µFC) networks in which each µFC network is associated with a distinguished connectivity pattern of recurrent neuronal activity. APPROACH The introduced approach is based on a multivariate Gaussian hidden Markov model (MGHMM) to decompose the sensor-space stochastic multi-subject event-related potential (ERP) into quasi-stable EEG microstates. Raw trial segments whose time windows belong to a corresponding segmented EEG microstate are then concatenated for measuring their µFC using the time-averaged phase-locking value. Illustration of this method is evaluated with synthetic data for which ground-truth microstate dynamics are known. Furthermore, we apply the method to identify EEG microstates and corresponding µFC networks in publicly available EEG data measured from visual cognitive tasks. Finally, we compare the MGHMM method with conventional dynamic FC (dFC) approaches using clustering-based K-means and time sliding windows, which conversely segregate the macrostate FC matrices across times into 'FC-states'. MAIN RESULTS By using the MGHMM approach, we reveal: (1) EEG microstates, (2) µFC networks, (3) the associations of EEG microstate networks and their corresponding µFC networks dynamically modulated in publicly available EEG cognitive tasks, and (4) compared dFC performances between our proposed µFC approaches and 'FC-states' segmented by clustering-based K-means and time sliding windows. SIGNIFICANCE Evidence of significant improvements of microstate correlations (p -value

Applications of entropy and the second law of thermodynamics in landscape ecology are rare and poorly developed. This is a fundamental limitation given the centrally important role the second law plays in all physical and biological processes. A critical first step to exploring the utility of thermodynamics in landscape ecology is to define the configurational entropy of a landscape mosaic. In this paper I attempt to link landscape ecology to the second law of thermodynamics and the entropy concept by showing how the configurational entropy of a landscape mosaic may be calculated. I begin by drawing parallels between the configuration of a categorical landscape mosaic and the mixing of ideal gases. I propose that the idea of the thermodynamic microstate can be expressed as unique configurations of a landscape mosaic, and posit that the landscape metric Total Edge length is an effective measure of configuration for purposes of calculating configurational entropy. I propose that the entropy of a given landscape configuration can be calculated using the Boltzmann equation. Specifically, the configurational entropy can be defined as the logarithm of the number of ways a landscape of a given dimensionality, number of classes and proportionality can be arranged (microstates) that produce the observed amount of total edge (macrostate).

An aggregated or ‘coarse-grained’ Markov chain (in discrete time and on a finite state-space) is a special case of a hidden Markov model, a type of model well known in the statistics literature and extensively applied in a wide variety of time-series or similar analyses. Such a coarse-grained Markov chain does not in general satisfy the Markov property, but recent work appearing in the physics and applied mathematics literature discusses relevant Markov-chain approximations, both at aggregated level and at microstate level, and establishes bounds on the approximation error. This note demonstrates that, for some purposes at least, such approximations are unnecessary; exact properties of hidden Markov models are available and can be used. In particular, the likelihood of the coarse-grained process can be computed routinely, and such a computation makes available various probabilities of interest associated with the process. Furthermore, this likelihood can be maximized numerically if there are unknown parameters and one has data from which one wishes to estimate them. This question of parameter estimation appears not to be addressed in the relevant literature.

International audience; Macroscopic pKa values were calculated for all compounds in the SAMPL6 blind prediction challenge, based on quantum chemical calculations with a continuum solvation model and a linear correction derived from a small training set. Microscopic pKa values were derived from the gas-phase free energy difference between protonated and deprotonated forms together with the Conductor-like Polarizable Continuum Solvation Model and the experimental solvation free energy of the proton. pH-dependent microstate free energies were obtained from the microscopic pKas with a maximum likelihood estimator and appropriately summed to yield macroscopic pKa values or microstate populations as function of pH. We assessed the accuracy of three approaches to calculate the microscopic pKas: direct use of the quantum mechanical free energy differences and correction of the direct values for short-comings in the QM solvation model with two different linear models that we independently derived from a small training set of 38 compounds with known pKa. The predictions that were corrected with the linear models had much better accuracy [root-mean-square error (RMSE) 2.04 and 1.95 pKa units] than the direct calculation (RMSE 3.74). Statistical measures indicate that some systematic errors remain, likely due to differences in the SAMPL6 data set and the small training set with respect to their interactions with water. Overall, the current approach provides a viable physics-based route to estimate macroscopic pKa values for novel compounds with reasonable accuracy.

Artificial spin ice (ASI) systems have emerged as promising hosts for magnonic applications due to a correspondence between their magnetic configuration and spin dynamics. Though it has been demonstrated that spin-wave spectra are influenced by the ASI microstate the precise nature of this relationship has remained unclear. Recent advances in controlling the magnetic configuration of ASI make harnessing the interplay between spin dynamics and the microstate achievable. This could allow diverse applications including reconfigurable magnonic crystals and programmable microwave filters. However, extracting any novel functionality requires a full understanding of the underlying spin-wave/microstate interaction. Here, we present a systematic analysis of how the microstate of a honeycomb ASI system affects its spin-wave spectrum through micromagnetic simulations. We find the spectrum to be highly tunable via the magnetic microstate, allowing the (de)activation of spin-wave modes and band-gap tuning via magnetic reversal of individual nanoislands. Symmetries of ASI systems and the chirality of ``monopole'' defects are found to play important roles in determining the high-frequency magnetic response.

Ambi-polar metrics, defined so as to allow the signature to change from +4 to -4 across hypersurfaces, are a mainstay in the construction of BPS microstate geometries. This paper elucidates the cohomology of these spaces so as to simplify greatly the construction of infinite families of fluctuating harmonic magnetic fluxes. It is argued that such fluxes should come from scalar, harmonic pre-potentials whose source loci are holomorphic divisors. This insight is obtained by exploring the Kahler structure of ambi-polar Gibbons-Hawking spaces and it is shown that differentiating the pre-potentials with respect to Kahler moduli yields solutions to the BPS equations for the electric potentials sourced by the magnetic fluxes. This suggests that harmonic analysis on ambi-polar spaces has a novel, and an extremely rich structure, that is deeply intertwined with the BPS equations. We illustrate our results using a family of two-centered solutions., Comment: 23 pages

Markov state models (MSMs) are a powerful framework for the analysis of molecular dynamics data sets, such as protein folding simulations, because of their straightforward construction and statistical rigor. The coarse-graining of MSMs into an interpretable number of macrostates is a crucial step for connecting theoretical results with experimental observables. Here we present the minimum variance clustering approach (MVCA) for the coarse-graining of MSMs into macrostate models. The method utilizes agglomerative clustering with Ward's minimum variance objective function, and the similarity of the microstate dynamics is determined using the Jensen-Shannon divergence between the corresponding rows in the MSM transition probability matrix. We first show that MVCA produces intuitive results for a simple tripeptide system and is robust toward long-duration statistical artifacts. MVCA is then applied to two protein folding simulations of the same protein in different force fields to demonstrate that a different number of macrostates is appropriate for each model, revealing a misfolded state present in only one of the simulations. Finally, we show that the same method can be used to analyze a data set containing many MSMs from simulations in different force fields by aggregating them into groups and quantifying their dynamical similarity in the context of force field parameter choices. The minimum variance clustering approach with the Jensen-Shannon divergence provides a powerful tool to group dynamics by similarity, both among model states and among dynamical models themselves.

While ubiquitous at all levels of organization in nature, including in nanotechnology, low-frequency 1/f noise is not yet understood. A possible reason is the unjustified application of probability theory concepts, primarily that of independence, to random physical phenomena. We show that in the framework of statistical mechanics, no medium can impart a definite diffusivity and mobility to a particle that performs random walk through it, which gives rise to flicker fluctuations in these properties. A universal source of 1/f noise in many-particle systems in this example is a dependence of the time behavior of any particular relaxation or transport process on the details of the initial microstate of the system as a whole.

We present general and rigorous results showing that the microcanonical and canonical ensembles are equivalent at all three levels of description considered in statistical mechanics - namely, thermodynamics, equilibrium macrostates, and microstate measures - whenever the microcanonical entropy is concave as a function of the energy density in the thermodynamic limit. This is proved for any classical many-particle systems for which thermodynamic functions and equilibrium macrostates exist and are defined via large deviation principles, generalizing many previous results obtained for specific classes of systems and observables. Similar results hold for other dual ensembles, such as the canonical and grand-canonical ensembles, in addition to path ensembles used for describing nonequilibrium systems driven in steady states., v1: 29 pages, 2 figures; v2: 31 pages, references added, minor changes to text and proofs, close to accepted version

Functions of biomolecules, in particular enzymes, are usually modulated by structural fluctuations. This is especially the case in a gated diffusion-controlled reaction catalyzed by an enzyme such as acetylcholinesterase. The catalytic triad of acetylcholinesterase is located at the bottom of a long and narrow gorge, but it catalyzes the extremely rapid hydrolysis of the neurotransmitter, acetylcholine, with a reaction rate close to the diffusion-controlled limit. Computational modeling and simulation have produced considerable advances in exploring the dynamical and conformational properties of biomolecules, not only aiding in interpreting the experimental data, but also providing insights into the internal motions of the biomolecule at the atomic level. Given the remarkably high catalytic efficiency and the importance of acetylcholinesterase in drug development, great efforts have been made to understand the dynamics associated with its functions by use of various computational methods. Here, we present a comprehensive overview of recent computational studies on acetylcholinesterase, expanding our views of the enzyme from a microstate of a single structure to conformational ensembles, strengthening our understanding of the integration of structure, dynamics and function associated with the enzyme, and promoting the structure-based and/or mechanism-based design of new inhibitors for it.

The adenosylcobalamin- (coenzyme B(12)) dependent ethanolamine ammonia-lyase (EAL) plays a key role in aminoethanol metabolism, associated with microbiome homeostasis and Salmonella- and Escherichia coli-induced disease conditions in the human gut. To gain molecular insight into these processes toward development of potential therapeutic targets, reactions of the cryotrapped (S)-2-aminopropanol substrate radical EAL from Salmonella typhimurium are addressed over a temperature (T) range of 220–250 K by using T-step reaction initiation and time-resolved, full-spectrum electron paramagnetic resonance spectroscopy. The observed substrate radical reaction kinetics are characterized by two pairs of biexponential processes: native decay to diamagnetic products and growth of a non-native radical species and Co(II) in cobalamin. The multicomponent low-T kinetics are simulated by using a minimal model, in which the substrate-radical macrostate, S(⋅), is partitioned by a free-energy barrier into two sequential microstates: 1) S(1)(⋅), a relatively high-entropy/high-enthalpy microstate with a protein configuration that captures the nascent substrate radical in the terminal step of radical-pair separation; and 2) S(2)(⋅), a relatively low-enthalpy/low-entropy microstate with a protein configuration that enables the rearrangement reaction. The non-native, destructive reaction of S(1)(⋅) at T ≤ 250 K is caused by a prolonged lifetime in the substrate-radical capture state. Monotonic S(⋅) decay over 278–300 K indicates that the free-energy barrier to S(1)(⋅) and S(2)(⋅) interconversion is latent at physiological T-values. Overall, the low-temperature studies reveal two protein-configuration microstates and connecting protein-configurational transitions that specialize the S(⋅) macrostate for the dual functional roles of radical capture and rearrangement enabling. The identification of new, to our knowledge, intermediate states and specific protein-fluctuation contributions to the reaction coordinate represent an advance toward development of novel therapeutic targets in EAL.

Analyses the efficiency of a WEB-Interfaced cloud computing module by using queuing theory, a microstate diagram for queuing system E 2 /M/M/n is shown and a program is developed to calculate the expected waiting time for services accounting cooling as part of the process.

We discuss the application of Siegel Modular Forms to Black Hole entropy counting. The role of the Igusa cusp form χ 10 in the D1D5P system is well-known, and its transformation properties are what allows precision microstate counting in this case. We apply a similar method to extract the Fourier coefficients of other Siegel modular and paramodular forms, and we show that they could serve as candidates for other types of black holes. We investigate the growth of their coefficients, identifying the dominant contributions and the leading logarithmic corrections in various regimes. We also discuss similarities and differences to the behavior of χ 10, and possible physical interpretations of such forms both from a microscopic and gravitational point of view., Journal of High Energy Physics, 2017 (4), ISSN:1126-6708, ISSN:1029-8479

We outline a systematic procedure to obtain horizonless microstate geometries that have the same charges as three-charge five-dimensional black holes with a macroscopically-large horizon area and an arbitrarily-small angular momentum. There are two routes through which such solutions can be constructed: using multi-center Gibbons-Hawking (GH) spaces or using superstratum technology. So far the only solutions corresponding to microstate geometries for black holes with no angular momentum have been obtained via superstrata, and multi-center Gibbons-Hawking spaces have been believed to give rise only to microstate geometries of BMPV black holes with a large angular momentum. We perform a thorough search throughout the parameter space of smooth horizonless solutions with four GH centers and find that these have an angular momentum that is generally larger than 80% of the cosmic censorship bound. However, we find that solutions with three GH centers and one supertube (which are smooth in six-dimensional supergravity) can have an arbitrarily-low angular momentum. Our construction thus gives a recipe to build large classes of microstate geometries for zero-angular-momentum black holes without resorting to superstratum technology., Comment: 36 pages, 23 figures; v2: minor corrections

We propose a novel strategy that permits the construction of completely general five-dimensional microstate geometries on a Gibbons-Hawking space. Our scheme is based on two steps. First, we rewrite the bubble equations as a system of linear equations that can be easily solved. Second, we conjecture that the presence or absence of closed timelike curves in the solution can be detected through the evaluation of an algebraic relation. The construction we propose is systematic and covers the whole space of parameters, so it can be applied to find all five-dimensional BPS microstate geometries on a Gibbons-Hawking base. As a first result of this approach, we find that the spectrum of scaling solutions becomes much larger when non-Abelian fields are present. We use our method to describe several smooth horizonless multicenter solutions with the asymptotic charges of three-charge (Abelian and non-Abelian) black holes. In particular, we describe solutions with the centers lying on lines and circles that can be specified with exact precision. We show the power of our method by explicitly constructing a 50-center solution. Moreover, we use it to find the first smooth five-dimensional microstate geometries with arbitrarily small angular momentum., Comment: 33 pages. v2: typos corrected

The notion of thermodynamic probability of a state ensures the number of microstates of a system, which provides the understanding of statistical entropy and ensemble of the system.

This chapter gives an introduction to the theoretical framework of molecular simulation studies provided by statistical mechanics Molecular simulations are aimed at predicting macroscopic thermophysical properties based on the behavior of the particles contained in the system. The detailed configuration of the system on the molecular level is called a microstate, and statistical mechanics is the theoretical framework that allows for determining macroscopic properties from studying the properties of the microstate.

A local approximation procedure for investigating the magnetic microstate of high-temperature superconductors is developed, which enables useful information to be obtained simultaneously on the crystal microstate of the sample. By probing the volume of the sample using an alternating attenuating magnetic field front, it becomes possible to isolate and investigate the physical processes in superconductors, which occur on the vortex front. Qualitatively new results are obtained for samples with different microstructures.

The intrinsic approach describing microscopic ionization equilibria is presented. This description massively reduces the number of parameters needed to characterize microequilibria. Particularly, by exploring molecular symmetries and group transferability, this approach is capable of resolving such equilibria even for rather complex molecules. Intrinsic constants are assigned to each ionizable group and interactions between these sites are introduced. These interactions involve pairs or triplets of sites. The strength of these interactions decreases rapidly with the distance between the sites. Once these parameters are known, one can obtain macroconstants, microconstants, microstate mole fractions, and overall or site-specific titration curves. These quantities provide insight into the protonation of the molecules in question. The knowledge of such properties is relevant for a wide range of phenomena, including receptor–ligand interactions, action of drugs, or geochemical processes.

In an Advanced Traveler Information System (ATIS), sensors are often used to monitor and obtain traffic information on a real-time basis. Knowing that traffic sensors cover only a fraction of the road network, the authors investigate how to estimate traffic volumes on arcs that are not covered by sensors. By exploiting the spatial properties and the topology of a network, they derive a microstate model that can be used to estimate these traffic volumes. Based on entropy maximization, they present a microstate surrogate for competing techniques such as traffic assignment, and algebraic method or topological approach in estimating traffic flow. Being an entropy model, it also has advantage over these competing techniques in terms of the prerequisite information required to enable the model. Being a microstate rather than a steady-state model, it takes into account the fluctuation of traffic and it executes fast enough to allow real-time estimation of traffic flow. By covering the entire network flow this way with only a limited number of sensors, it will help in better driver routing decisions and traffic management tactics while being cognizant of today’s budgetary constraints facing operating agencies. The algorithm has been tested successfully in Little Rock, Arkansas and in a controlled experiment with a randomly generated 100-node/522-arc grid network.

In this paper, we discuss that an observable-based single-system Copenhagen and entanglement-based two-system von Neumann measurement protocols in quantum theory can be made equivalent by considering the second part of the two-system scheme to be a Dirac-type negative sea filling up the first system. Based on this equivalence, and by considering the universe as a computational process, the choice of the apparatus state in the two-system protocol can be identified with the choice of the observable in the single-system scheme as negative sea filling up the observable universe. In particular, the measuring party's state is considered to be evolving backwards in time to the big bang as a nondeterministic computational process, which chooses the acceptable path as a time-reversal process of irreversible computation. The suggested model proposes that the prepared microstate of the universe, or reality, corresponds to the observer's choice, therefore, subjective reality. Thus, this effectively provides a specific description of the subjective universe model previously proposed, which is based on the symmetry breakdown between the Schrodinger and the Heisenberg pictures of quantum theory.

We present results for the determination of the equilibrium microstate probability distribution of a class of strongly interacting systems obeying stochastic dynamics but without the necessity of detailed balance. The specific case of Ising systems is highlighted, with applications to non-symmetric synaptic neural networks and more general recurrent Boolean networks.

Can a popular real-world competition system indeed be fragile? To address this question, we represent such a system by a directed binary network. Upon observed network data, typically in a form of win-and-loss matrix, our computational developments begin with collectively extracting network's information flows. And then we compute and discover network's macrostate. This computable macrostate is further shown to contain deterministic structures embedded with randomness mechanisms. Such coupled deterministic and stochastic components becomes the basis for generating the microstate ensemble. Specifically a network mimicking algorithm is proposed to generate a microstate ensemble by subject to the statistical mechanics principle: All generated microscopic states have to conform to its macrostate of the target system. We demonstrate that such a microstate ensemble is an effective platform for exploring systemic sensitivity. Throughout our computational developments, we employ the NCAA Football Bowl Subdivision (FBS) as an illustrating example system. Upon this system, its macrostate is discovered by having a nonlinear global ranking hierarchy as its deterministic component, while its constrained randomness component is embraced within the nearly completely recovered conference schedule . Based on the computed microstate ensemble, we are able to conclude that the NCAA FBS is overall a fragile competition system because it retains highly heterogeneous degrees of sensitivity with its ranking hierarchy.

The two criteria of ensemble equivalence, i.e. the macrostate equivalence and the measure equivalence, are investigated for a general pair of states. The macrostate equivalence implies the two ensembles are indistinguishable by the measurement of macroscopic quantities obeying the large-deviation principle, and the measure equivalence means that the specific relative entropy of these two states vanishes in the thermodynamic limit. It is shown that the measure equivalence implies the macrostate equivalence for a general pair of states by deriving an inequality connecting the large-deviation rate functions to the specific relative Renyi entropies. The result is applicable to both quantum and classical systems. As applications, a sufficient condition for thermalization, the timescale of quantum dynamics of macrovariables, and the second law with strict irreversibility in a quantum quench are discussed., 6 pages

Molecular dynamics systems evolve through the interplay of collective and localized disturbances. As a practical consequence, there is a restriction on the time step imposed by the broad spectrum of time scales involved. To resolve this restriction, multiscale factorization was introduced for molecular dynamics as a method that exploits the separation of time scales by coevolving the coarse-grained and atom-resolved states via Trotter factorization. Developing a stable time-marching scheme for this coevolution, however, is challenging because the coarse-grained dynamical equations depend on the microstate; therefore, these equations cannot be expressed in closed form. The objective of this paper is to develop an implicit time integration scheme for multiscale simulation of large systems over long periods of time and with high accuracy. The scheme uses Pade approximants to account for both the stochastic and deterministic features of the coarse-grained dynamics. The method is demonstrated for a protein either undergoing a conformational change or migrating under the influence of an external force. The method shows promise in accelerating multiscale molecular dynamics without a loss of atomic precision or the need to conjecture the form of coarse-grained governing equations.

The study object is wheat. Through the observation and analysis on the morphological structure of wheat plant, the concepts of microstate, substrate and microstate are put forward, the wheat growth mechanism model is established, and thus the description and control of wheat morphogenesis process could be realized. Based on the branch structure characteristics of plant, the wheat morphological data model based on axis structure is proposed to realize the structural storage of plant topological structure and organ morphological feature data. On this basis, based on the thought of "growth model - morphological feature model - geometric modeling - display model", the technical framework of wheat form visualization is established and on the VC++ platform, the virtual wheat growth system is built with OpenGL. The running result of the system shows that wheat morphological feature can be well simulated with the system to realize the virtual display of the growth process in the individual growth period of wheat.

The statistical mechanics of dynamical systems on which only isotropic viscous friction forces act is developed. A non-stationary analogue of the Gibbs canonical distribution, which enables each such system to be made to correspond to a certain thermodynamic system that satisfies the first and second laws of thermodynamics, is introduced. The evolution of non-Gibbs probability distributions with time is also considered.