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Disordered biopolymer gels, such as those synthesized from polysaccharide and gelatin, play an important role in biomedical applications, particularly in tissue engineering. During the gelation process of these gels, polymer chains associate in the presence of gelling agents, forming physical cross-links known as the junction zones. In contrast to rubber-like networks, the resulting network comprises two main regions: the ordered region due to the junction zones and the amorphous region due to the unassociated chains. Under thermal fluctuations and/or external loading, the number and locations of junction zones can change leading to "zipping" (lengthening, i.e., expansion of the junction zones) and "unzipping" (shortening, i.e., shrinkage of the junction zones). This gives rise to intriguing features in biopolymer gels such as healing and damage-like energy dissipation. Despite the recognition of zipping and unzipping in such gels, the development of mathematical models that incorporate the microscopic mechanisms into the material's macroscopic mechanical properties is still in its early stages. In this paper, we provide a systematic framework for such multiscale modeling. Several critical steps are taken to equip the eight-chain network model with a previously developed micromechanics model for a coil–rod structure, where the coil represents an unassociated chain and the rod represents a junction zone. Most importantly, for a network of coil–rod structures under zero stress, the rigidity induced by the rod leads to an end-to-end distance (r 0) for the coil–rod which is different from a classical result for a Gaussian coil: n b where b is the Kuhn length and n is the number of Kuhn segments in the coil. By relaxing the incompressible assumption in the original eight-chain model, r 0 is determined for the gel network, which depends on the length of the junction zone. Consequently, as the junction zone extends/shrinks following zipping/unzipping under an external load, an irreversible deformation can occur after unloading, consistent with experimentally observed "permanent set". The extension/shrinkage of the junction zone is captured by statistical mechanics analysis in the grand canonical ensemble, which allows the exchange of segments between the coil and the rod, driven by the binding energy of polymer chain association. The model also includes explicit consideration of swelling and the influence of solvent molecules as a result of their mixing with the polymer chains in the gel network. With physically reasonable parameters, the proposed model is shown to provide good matching with experimental data on the uniaxial testing of alginate gels, revealing progressive unzipping during loading and partial re-zipping during unloading leading to the appearance of a permanent set. This formulation not only paves the way for more advanced studies of disordered biopolymer gels but also lays the groundwork for modeling hybrid gels that contain coil–rod structures as a component. [ABSTRACT FROM AUTHOR]

Thermal-FIST 1 1 Thermal-FIST — Thermal, Fast and Interactive Statistical Toolkit. is a C++ package designed for convenient general-purpose physics analysis within the family of hadron resonance gas (HRG) models. This mainly includes the statistical analysis of particle production in heavy-ion collisions and the phenomenology of hadronic equation of state. Notable features include fluctuations and correlations of conserved charges, effects of probabilistic decay, chemical non-equilibrium, and inclusion of van der Waals hadronic interactions. Calculations are possible within the grand canonical ensemble, the canonical ensemble, as well as in mixed-canonical ensembles combining the canonical treatment of certain conserved charges with the grand-canonical treatment of other conserved charges. The package contains a fast thermal event generator, which generates particle yields in accordance with the HRG chemistry, and particle momenta based on the Blast Wave model. A distinct feature of this package is the presence of the graphical user interface frontend – QtThermalFIST – which is designed for fast and convenient general-purpose HRG model applications. Program Title: Thermal-FIST , version 1.2 Program Files doi: http://dx.doi.org/10.17632/pprr8p4fkp.1 Licensing provisions: GPLv3 Programming language: C++ External routines: Eigen template library for the linear algebra routines [1], MINUIT2 package from CERN ROOT [2], Mersenne Twister random number generator [3], Qt5 framework [4] (for the GUI only), QCustomPlot Qt widget [5] (for the GUI only) Nature of problem: The HRG model and its various modifications constitute a common framework used for modeling of the hadronic equation of state and particle production in heavy-ion collisions. Even the simplest versions of the HRG model require careful considerations of the many details, including the resonance decay feed-down, implementation of charge conservation constraints relevant for heavy-ion collisions, chemical non-equilibrium effects. A notable extra effort is required in order to treat the fluctuations and correlations of various charges , which presently are being extensively studied in the heavy-ion collision experiments and lattice QCD calculations. The inclusion of hadronic interactions, modeled by an excluded-volume (EV) or a van der Waals (vdW) type framework, additionally requires a numerical solution to a system of many transcendental equations. Solution method: The Thermal-FIST package contains a class-based library which calculates relevant HRG observables for a specified setup. The setup includes a particle list, usually to be supplied with an external file, an HRG model specification (statistical ensemble, van der Waals interaction parameters, etc.), a set of thermal parameters, and conservation laws constraints. Whenever necessary, the systems of transcendental equations are solved numerically with the Broyden's method. The package includes a fitter for extracting thermal parameters from hadron yield data through the χ 2 minimization. The HRG model based Monte Carlo event generator is a complementary feature to analytic calculations. A general-purpose thermal analysis is made maximally convenient with QtThermalFIST — a GUI frontend based on the Qt framework where all typical calculations, such as the properties of the equation of state or the thermal fits, can be straightforwardly performed. Additional comments: If the EV/vdW interactions are present, exact analytic calculations are presently only possible within the grand canonical ensemble. Approximate calculations are possible for the strangeness-canonical ensemble on the condition that strange particles form a small subsystem relative to the total system. Effects of probabilistic decays on fluctuation observables are generally included only up to the moments of the 2nd order. The only exception is the ideal HRG model in the grand canonical ensemble, where these effects are included up to the moments of the 4th order. On the other hand, the Monte Carlo event generator is not constrained by the above restrictions. References: [1] http://eigen.tuxfamily.org [2] https://project-mathlibs.web.cern.ch/project-mathlibs/sw/Minuit2/html/ [3] M. Matsumoto, T. Nishimura, Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator, ACM Transactions on Modeling and Computer Simulation (TOMACS), 8 (1998) 3; Implementation by R. J. Wagner: http://www.math.sci.hiroshima-u.ac.jp/ m-mat/MT/VERSIONS/C-LANG/MersenneTwister.h [4] https://www.qt.io [5] https://www.qcustomplot.com/ [ABSTRACT FROM AUTHOR]

We determine the regime where the widespread classical field description for quantum Bose gases is quantitatively accurate in one dimension (1D), 2D, and 3D by a careful study of the ideal gas limit. Numerical benchmarking in 1D shows that the ideal gas results carry over unchanged into the weakly interacting gas. The optimum high-energy cutoff is in general shown to depend strongly on the observable in question (e.g., energy, density fluctuations, phase coherence length, condensate fraction). This explains the wide range of past results. A consistent classical field representation with less than 10% deviation in all typical observables can be given for systems at temperatures below 0.0064 degeneracy temperature in 1D, and 0.49 critical temperature in 3D. Surprisingly, this is not possible for the two-dimensional ideal gas even at zero temperature because mean density, density fluctuations, and energy cannot be simultaneously matched to the quantum results. [ABSTRACT FROM AUTHOR]

Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the auxiliary-field Monte Carlo (AFMC) method, low-temperature or large-model-space calculations require numerically stabilized matrix multiplication. When adapting methods used in the grand-canonical ensemble to the canonical ensemble of fixed particle number, the numerical stabilization increases the number of required floating-point operations for computing observables by a factor of the size of the single-particle model space, and thus can greatly limit the systems that can be studied. We describe an improved method for stabilizing canonical-ensemble calculations in AFMC that exhibits better scaling, and present numerical tests that demonstrate the accuracy and improved performance of the method. [ABSTRACT FROM AUTHOR]

In this paper noncommutative gravity is constructed as a gauge theory of the noncommutative SO(2,3) group, while the noncommutativity is canonical (constant). The Seiberg-Witten map is used to express noncommutative fields in terms of the corresponding commutative fields. The commutative limit of the model is the Einstein-Hilbert action with the cosmological constant term and the topological Gauss-Bonnet term. We calculate the second order correction to this model and obtain terms that are of zeroth to fourth power in the curvature tensor and torsion. Trying to relate our results with ƒ(R) and ƒ(T) models, we analyze different limits of our model. In the limit of big cosmological constant and vanishing torsion we obtain an x-dependent correction to the cosmological constant; i.e. noncommutativity leads to an x-dependent cosmological constant. We also discuss the limit of small cosmological constant and vanishing torsion and the teleparallel limit. [ABSTRACT FROM AUTHOR]

It is widely believed that the stationary properties after a quantum quench in integrable systems can be described by a generalized Gibbs ensemble (GGE), even if all of the analytical evidence is based on free theories in which the pre- and postquench modes are linearly related. In contrast, we consider the experimentally relevant quench of the one-dimensional Bose gas from zero to infinite interaction, in which the relation between modes is nonlinear, and consequently Wick's theorem does not hold. We provide exact analytical results for the time evolution of the dynamical density-density correlation function at any time after the quench and we prove that its stationary value is described by a GGE in which Wick's theorem is restored. [ABSTRACT FROM AUTHOR]

Abstract: This work describes an implementation of canonical and Gibbs ensemble Monte Carlo simulations on graphics processing units (GPUs). The pair-wise energy calculations, which consume the majority of the computational effort, are parallelized using the energetic decomposition algorithm. While energetic decomposition is relatively inefficient for traditional CPU-bound codes, the algorithm is ideally suited to the architecture of the GPU. The performance of the CPU and GPU codes are assessed for a variety of CPU and GPU combinations for systems containing between 512 and 131,072 particles. For a system of 131,072 particles, the GPU-enabled canonical and Gibbs ensemble codes were 10.3 and 29.1 times faster (GTX 480 GPU vs. i5-2500K CPU), respectively, than an optimized serial CPU-bound code. Due to overhead from memory transfers from system RAM to the GPU, the CPU code was slightly faster than the GPU code for simulations containing less than 600 particles. The critical temperature and density were determined for the tail corrected Lennard-Jones potential from simulations of 10,000 particle systems, and found to be in exact agreement with prior mixed field finite-size scaling calculations [J.J. Potoff, A.Z. Panagiotopoulos, J. Chem. Phys. 109 (1998) 10914]. [Copyright &y& Elsevier]

We derive the expressions for canonical energy, momentum, and angular momentum for multiple metric theories. We prove that although the metric fields are generally interacting, the total energy is the sum of conserved energies corresponding to each metric. A positive energy theorem is given as a result. In addition, we present an Hamiltonian formalism for a subgroup of multimetric theories. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a scheme for the canonical ensemble simulation of the coarse-grained articulated polymers is discussed. In this coarse-graining strategy, different subdomains of the system are considered as rigid and/or flexible bodies connected to each other via kinematic joints instead of stiff, but elastic bonds. Herein, the temperature of the simulation is controlled by a Nosé–Hoover thermostat. The dynamics of this feedback control system in the context of multibody dynamics may be represented and solved using traditional methods with computational complexity of where denotes the number of degrees of freedom of the system. In this paper, we extend the divide-and-conquer algorithm (DCA), and apply it to constant temperature molecular simulations. The DCA in its original form uses spatial forces to formulate the equations of motion. The Generalized-DCA applied here properly accommodates the thermostat generalized forces (from the thermostat), which control the temperature of the simulation, in the equations of motion. This algorithm can be implemented in serial and parallel with computational complexity of and , respectively. [Copyright &y& Elsevier]

A constant-(N,V,T,θ) ensemble is proposed to describe the elastostatics of random solid structures. Within the harmonic approximation, the energy of such a solid structure is the sum of a thermal and a strain component without mutual interaction. Systems in this ensemble thus draw energies from two separate baths: one thermal and the other mechanical. A mechanical entropy and an effective temperature (θ) can then be defined on the same rigorous basis as the thermal entropy and the Kelvin temperature (T). This ensemble approach can be used to calculate the properties of solid structures sharing similar microstructural randomness. [Copyright &y& Elsevier]

Maggiore observed that, in the high-damping regime, the quasinormal modes spectrum for the Schwarzschild black hole resembles that of a quantum harmonic oscillator. Motivated by this observation, we describe a black hole as a statistical ensemble of N quantum harmonic oscillators. By working in the canonical ensemble, we show that, in the large-mass black hole limit, the leading contribution to the Gibbs entropy is the Bekenstein-Hawking term, while the subleading one is a logarithmic correction, in agreement with several results in the literature. We also find that the number of oscillators scales holographically with the area of the event horizon. [ABSTRACT FROM AUTHOR]

We obtain two types of Yang-Mills-dilaton black hole solutions in both Lifshitz and hyperscaling violation spacetimes. We must consider at least three Yang-Mills gauge fields that interact with a scalar field and either SO(n) or SO (n-1, 1) gauge symmetry groups, where n+1 denotes the dimension of the spacetime. They lead to the spherical and hyperbolic solutions. The obtained solutions in the hyperscaling violation spacetime fall into two categories for z≠n-3-n-5/n-1θ and z=n-3-n-5/n-1θ, where θ=0 represents the Lifshitz spacetime. In order to have a real asymptotic behavior for the hyperscaling violated black hole solutions, we should consider a negative value for the hyperscaling violation parameter as θ<0. We also evaluate the thermodynamic quantities of the mentioned black holes and probe their thermal stability in the grand canonical ensemble. For z≥2, the hyperscaling violated solutions are not thermally stable for z≤n-3-n-5/n-1θ, while they are stable for large r+ with z>n-3-n-5/n-1θ. We also check out the critical behavior of the obtained black holes and obtain a Smarr relation for the solutions. The results also announce of a first-order small-large phase transition for both black holes in the case T>TC. [ABSTRACT FROM AUTHOR]

We present and discuss a new family of topological hairy dyonic black hole solutions in asymptotically anti-de Sitter space. The coupled Einstein-Maxwell-scalar gravity system, that carries both the electric and magnetic charges is solved, and exact hairy dyonic black hole solutions are obtained analytically. The scalar field profiles that give rise to such black hole solutions are regular everywhere. The hairy solutions are obtained for planar, spherical, and hyperbolic horizon topologies. In addition, analytic expressions of regularized action, stress tensor, conserved charges, and free energies are obtained. We further comment on different prescriptions for computing the black hole mass with hairy backgrounds. We analyze the thermodynamics of these hairy dyonic black holes in canonical and grand canonical ensembles, and we find that both electric and magnetic charges have a constructive effect on the stability of the hairy solution. For the case of planar and hyperbolic horizons, we find thermodynamically stable hairy black holes that are favored at low temperatures compared to the nonhairy counterparts. We further find that, for a spherical hairy dyonic black hole, the thermodynamic phase diagram resembles to that of a Van der Waals fluid not only in canonical but also in the grand canonical ensemble. [ABSTRACT FROM AUTHOR]

In this work we show that Einstein gravity in four dimensions can be consistently obtained from the compactification of a generic higher curvature Lovelock theory in dimension D=4+p, (p≥1). The compactification is performed on a direct product space MD=M4×Kp, where Kp is a Euclidean internal manifold of constant curvature. The process is carried out in such a way that no fine tuning between the coupling constants is needed. The compactification requires us to dress the internal manifold with the flux of suitable p-forms whose field strengths are proportional to the volume form of the internal space. We explicitly compactify Einstein-Gauss-Bonnet theory from dimension six to Einstein theory in dimension four and sketch out a similar procedure for this compactification to take place starting from dimension five. Several black string/p-branes solutions are constructed, among which, a five dimensional asymptotically flat black string composed of a Schwarzschild black hole on the brane is particularly interesting. Finally, the thermodynamic of the solutions is described and we find that the consistent compactification modifies the entropy by including a constant term, which may induce a departure from the usual behavior of the Hawking-Page phase transition. New scenarios are possible in which large black holes dominate the canonical ensemble for all temperatures above the minimal value. [ABSTRACT FROM AUTHOR]

We study thermodynamics and critical behaviors of higher-dimensional Lovelock black holes with nonmaximally symmetric horizons in the canonical ensemble of extended phase space. The effects from nonconstancy of the horizon of the black hole via appearing two chargelike parameters in thermodynamic quantities of third-order Lovelock black hole are investigated. We find that Ricci flat black holes with nonconstant curvature horizon show critical behavior. This is an interesting feature that is not seen for any kind of black hole in Einstein or Lovelock gravity in the literature. We examine how various interesting thermodynamic phenomena such as standard first-order small-large black hole phase transition, a reentrant phase transition, or zeroth order phase transition happen for Ricci flat, spherical, or hyperbolic black holes with nonconstant curvature horizon depending on the values of Lovelock coefficient and chargelike parameters. While for a spherical black hole of third order Lovelock gravity with constant curvature horizon phase transition is observed only for 7≤d≤11, for our solution criticality and phase transition exist in every dimension. With a proper choice of the free parameters, a large-small-large black hole phase transition occurs. This process is accompanied by a finite jump of the Gibbs free energy referred to as a zeroth-order phase transition. For the case κ=-1 a novel behavior is found for which three critical points could exist. [ABSTRACT FROM AUTHOR]

In the context of black hole chemistry (BHC), holographic phase transitions of asymptotically anti-de Sitter (AdS) charged topological black holes (TBHs) in massive gravity coupled to power Maxwell invariant (PMI) electrodynamics are discussed in the grand canonical (fixed U(1) potential, Φ) ensemble. Considering the higher-order of graviton's self-interactions of (dRGT) massive gravitational field theory in arbitrary dimensions, we derive exact TBH solutions. We also calculate the explicit form of the on-shell action and the associated thermodynamic quantities in the grand canonical ensemble (GCE). Besides, we examine the validity of the first law of thermodynamics and Smarr relation in the extended phase space thermodynamics. Regarding this model, we show that (a) a van der Waals (vdW) behavior takes place in d≥4 dimensions, (b) a typical reentrant phase transition can happen in d≥5, and (c) both anomalous vdW and triple point phenomena are recognized in d≥6. Accordingly, we find that the obtained results are quite different from their counterparts in the GCE of Maxwell-massive gravity. Furthermore, we briefly study the critical behaviors of higher-dimensional TBHs with a conformally invariant Maxwell source as a specific subclass of our solutions for Einstein's theory and the massive gravity in various ensembles. [ABSTRACT FROM AUTHOR]

The auxiliary-field quantum Monte Carlo (AFMC) method is a powerful and widely used technique for ground-state and finite-temperature simulations of quantum many-body systems. We introduce several algorithmic improvements for finite-temperature AFMC calculations of dilute fermionic systems that reduce the computational complexity of most parts of the algorithm. This is principally achieved by reducing the number of single-particle states that contribute at each configuration of the auxiliary fields to a number that is of the order of the number of fermions. Our methods are applicable for both the canonical and grand-canonical ensembles. We demonstrate the reduced computational complexity of the methods for the homogeneous unitary Fermi gas. [ABSTRACT FROM AUTHOR]

Two-particle momentum correlations of N identical bosons are studied in the quantum canonical ensemble. We define the latter as a properly selected subensemble of events associated with the grand canonical ensemble which is characterized by a constant temperature and a harmonic-trap chemical potential. The merits of this toy model are that it can be solved exactly, and that it demonstrates some interesting features revealed recently in small systems created in p+p collisions at the LHC. We find that partial coherence can be observed in particle emission from completely thermal ensembles of events if instead of inclusive measurements one studies the two-boson distribution functions related to the events with particle numbers selected in some fixed multiplicity bins. The corresponding coherence effects increase with the multiplicity. [ABSTRACT FROM AUTHOR]

We study the thermodynamic properties of a two-site coupled complex q-body Sachdev-Ye-Kitaev (SYK) model in the large-N limit by solving the saddle-point Schwinger-Dyson (SD) equations. We find that its phase diagram is richer than in the Majorana case. In the grand canonical ensemble, we identify a region of small chemical potential and weak coupling between the two SYKs, for which two first order thermodynamic phase transitions occur as a function of temperature. First, we observe a transition from a cold wormhole phase to an intermediate phase that may correspond to a charged wormhole. For a higher temperature, there is another first order transition to the black hole phase. As in the Majorana case, the low temperature wormhole phase is gapped, and for sufficiently large coupling between the two complex SYK, or chemical potential, the first order transitions become crossovers. The total charge is a good indicator to study the phase diagram of the model; it is zero in the cold wormhole phase and jumps discontinuously at the temperatures at which the transitions take place. Based on the approximate conformal symmetry of the ground state, expected to be close to a thermofield double state, we identify the effective low energy action of the model. It is a generalized Schwarzian action with SL(2,R)×U(1) symmetry with an additional potential and an extra degree of freedom related to the charge. In the large N and low temperature limit, results from this low energy action are consistent with those from the solution of the SD equations. Likewise, a large-q analytical calculation of thermodynamic properties confirms the existence of the wormhole phase. Our findings are a preliminary step toward the characterization of traversable wormholes by its field theory dual, a charged strongly interacting fermionic system, that is easier to model experimentally. [ABSTRACT FROM AUTHOR]

We study the thermodynamics of a d-dimensional Schwarzschild black hole, also known as a Schwarzschild-Tangherlini black hole, in the canonical ensemble. This generalizes York's formalism, which has been initially applied to four dimensions and later to five dimensions, to any number d of dimensions. The canonical ensemble, characterized by a cavity of fixed radius r and fixed temperature T at the boundary, allows for two possible black hole solutions in thermal equilibrium, a smaller black hole and a larger black hole. In four and five dimensions, these solutions have a direct exact form, whereas in an arbitrary number of dimensions, one is compelled to resort to approximation schemes or numerical calculations. From the Euclidean action and the path integral approach, we obtain the free energy, the thermodynamic energy, the thermodynamic pressure, and the entropy, of the black hole plus cavity system. The entropy of the system is given by the Bekenstein-Hawking area law. The analysis of the heat capacity of the system shows that the smaller black hole is in unstable equilibrium and the larger black hole is in stable equilibrium. The d-dimensional photon sphere radius divides the stability criterion. Indeed, if the cavity's radius is larger than the photon sphere radius, and so the black hole is small, the system is unstable, if the cavity's radius is smaller than the photon sphere radius, and so the black hole is large, the system is stable. To study perturbations on the system, a generalized free energy function is obtained that also allows one to understand the possible phase transitions between classical hot flat space and the black holes. The Buchdahl radius, that appears naturally in the general relativistic study of star structure, also shows up in our context; the free energy is zero when the cavity's radius has the d-dimensional Buchdahl radius value. Then, if the cavity's radius is larger than the Buchdahl radius, classical hot flat space phase cannot make a phase transition to a black hole phase, and if smaller, classical hot flat space can nucleate a black hole. The roles of both the photon sphere and the Buchdahl limit are present for every dimension d, indicating that, besides their known role in dynamics, these radii also play a role in the thermodynamics of gravitational systems. The close link between the canonical analysis performed and the direct perturbation of the path integral is also pointed out. Since hot flat space is a quantum system made purely of gravitons, if only gravitation is considered, it is of great interest to compare the d-dimensional free energies of quantum hot flat space and the stable black hole to find for which ranges of r and T, the quantities that characterize the canonical ensemble, one phase predominates over the other. Phase diagrams for a few different dimensions are displayed. The density of states at a given energy is found through an inverse Laplace transformation giving back the entropy of the stable black hole. Several side calculations and further deliberations are performed, namely, the calculation for the approximate expressions for the canonical ensemble black hole horizon radii, a brief study of the photon orbit radius and the Buchdahl radius in the d-dimensional Schwarzschild solution, a connection to the thermodynamics of thin shells in d spacetime dimensions which are systems that are also apt to a rigorous thermodynamic study, a presentation of quantum hot flat space in d spacetime dimensions as a thermodynamic system, an analysis of classical hot flat space in d spacetime dimensions as a product of quantum hot flat space with the black hole transitions and the corresponding phase diagrams for a few different dimensions, and a synopsis with the relevance of the work. It is still worth mentioning that the comparison of the thermodynamics of d-dimensional Schwarzschild black holes and classical hot flat space in the canonical ensemble with the thermodynamics of spherical thin shells in d dimensions yields a striking direct matching between the two systems, most notably that the photon sphere radius appears here as a thermodynamic stability divisor in both systems, and the Buchdahl radius that appears on thermodynamic grounds for canonical black holes appears also as a thermodynamic and as a dynamical radius for thin shells. [ABSTRACT FROM AUTHOR]

This paper argues that the weak cosmic censorship hypothesis implies that the Schwarzschild black hole has maximal entropy in all stationary black holes of fixing temperature, or equivalently, to store a same amount of information the Schwarzschild black hole has highest temperature. It then gives the independent mathematical proofs for 4-dimensional general static black holes and stationary-axisymmetric black holes which have "t -" reflection isometry. This result does not only provide a new universal bound between temperature and entropy of black holes but also offers us new evidence to support the weak cosmic censorship hypothesis. [ABSTRACT FROM AUTHOR]

In this paper, we study the small-large black hole phase transition and construct the Ruppeiner geometry for the five-dimensional charged Gauss-Bonnet-AdS black hole in the grand canonical ensemble. By making use of the equal area law, we obtain the analytical coexistence curve of the small and large black holes. Then the phase diagrams are examined. We also calculate the change of the thermodynamic volume during the small-large phase transition, which indicates that there exists a sudden change among the black hole microstructures. The corresponding normalized scalar curvature of the Ruppeiner geometry is also calculated. Combing with the empirical observation of scalar curvature, we find that for low electric potential, the attractive interaction dominates among the microstructures, while a high electric potential produces repulsive interactions. In the reduced parameter space, we observe that only attractive interaction is allowed when the coexistence region is excluded. The normalized scalar curvature also admits a critical exponent 2 and a universal constant -1/8. In particular, the value of the normalized scalar curvature keeps the same along the coexistence small and large black hole curves. So in the grand canonical ensemble, the interaction can keep constant at the phase transition where the black hole microstructures change. These results disclose the intriguing microstructures for the charged AdS black hole in the Gauss-Bonnet gravity. [ABSTRACT FROM AUTHOR]

• Direct coupling of Molecular Dynamics to Direct Simulation Monte Carlo for HPC. • Developed in open-source software OpenFOAM and the Multiscale Universal Interface. • New capability to simulate complex problems using DSMC and MD. • Part of ongoing work to create a tri-scale coupled methodology. A domain-decomposed method to simultaneously couple the classical Molecular Dynamics (MD) and Direct Simulation Monte Carlo (DSMC) methods is proposed. This approach utilises the MPI-based general coupling library, the Multiscale Universal Interface. The method provides a direct coupling strategy and utilises two OpenFOAM based solvers, mdFoam+ and dsmcFoam+, enabling scenarios where both solvers assume one discrete particle is equal to one molecule or atom. The ultimate goal of this work is to enable complex multi-scale simulations involving micro, meso and macroscopic elements, as found with problems like evaporation. Results are presented to show the fundamental capabilities of the method in terms of mass and kinetic energy conservation between simulation regions handled by the different solvers. We demonstrate the capability of the method by deploying onto a large supercomputing resource, with attention paid to the scalability for a canonical NVT ensemble (a constant number of atoms N , constant volume V and constant temperature T) of Argon atoms. The results show that the method performs as expected in terms of mass conservation and the solution is also shown to scale reasonably on a supercomputing resource, within the known performance limits of the coupled codes. The wider future of this work is also considered, with focus placed on the next steps to expand the capabilities of the methodology to allow for indirect coupling (where the coarse-graining capability of the DSMC method is used), as well as how this will then fit into a larger coupled framework to allow a complete micro-meso-macro approach to be tackled. [ABSTRACT FROM AUTHOR]

• Interaction of a solute atmosphere with a void: a statistical mechanics approach. • Modeling solute atmosphere as a distribution of misfitting solute rods in the host. • Monte Carlo simulations of the solute atmosphere accounting for interaction effects. • Numerical and analytical calculation of ensemble average of energy release rates. • Interaction with external loading: solute redistribution and role of image stresses. Solid solutions are of critical importance to many technological applications. While continuum frameworks have been developed and invoked in the past for studying behavior of solid solutions, recent studies point to the importance of image stresses in finite systems, and in particular, suggest that the homogenized self-stress field of the solutes, which enter the chemical potential in the prevalent continuum models, should be excluded in a correct treatment. The present work is concerned with the study of a solute atmosphere in the vicinity of a void in two-dimensional elasticity wherein the solute atmosphere is treated as a distribution of solute rods extended indefinitely normal to the plane of analysis. A statistical mechanics framework is adopted based on the Gibbs canonical ensemble, and the well-established path-independent integrals of solid mechanics are used for examining configurational forces on the void induced by the presence of a solute atmosphere. Numerical Monte Carlo simulations fully accounting for the interaction energy between the solute rods are used for calculation of the ensemble averages of the energy release rates associated with void translation and expansion, and semi-analytical solutions are further developed in the limit of dilute solute concentrations and large temperatures. Effect of interaction between the stress fields of a solute atmosphere and an external loading on the configurational forces is also investigated through both numerical and analytical calculations. It is shown that the interaction between the image stress field of a given concentration of solute rods and the stress field of an equi-biaxial loading results in an added contribution to the energy release rate of void expansion which does not fade away even when the solid dimensions grow indefinitely. Numerical simulations are further used to examine the effect of loading-induced solute redistribution on the energetic driving force for void expansion. [ABSTRACT FROM AUTHOR]

We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at large length scales. The partition function diverges and hence the standard canonical ensemble fails. This is replaced with tools stemming from infinite ergodic theory. Boltzmann-Gibbs statistics, even though not normalized, still describes integrable observables, like energy and occupation times. The Boltzmann infinite density is derived heuristically using an entropy maximization principle, as well as via a first-principles calculation using an eigenfunction expansion in the continuum of low-energy states. A generalized virial theorem is derived, showing how the virial coefficient describes the delay in the diffusive spreading of the particles, found at large distances. When the process is non-recurrent, e.g. diffusion in three dimensions with a Coulomb-like potential, we use weighted time averages to restore basic canonical relations between time and ensemble averages. [ABSTRACT FROM AUTHOR]

We study the thermodynamics of a five-dimensional Schwarzschild black hole, also known as a five-dimensional Schwarzschild-Tangherlini black hole, in the canonical ensemble using York's formalism. Inside a cavity of fixed size r and fixed temperature T, we find that there is a threshold at πrT=1 above which a black hole can be in thermal equilibrium with the cavity's boundary. Moreover, this thermal equilibrium can only be achieved for two specific types of black holes. One is a small black hole (compared with the cavity size r) of horizon radius r+1, while the other is a large black hole (of the order of the cavity size r) of horizon radius r+2. In five dimensions, the radii r+1 and r+2 have an exact expression. Through the path integral formalism, which directly yields the partition function of the system, one obtains the action and thus the free energy for the black hole in the canonical ensemble. The procedure leads naturally to the thermal energy and entropy of the canonical system, the latter turning out to be given by the Bekenstein-Hawking area law S=A+4, where the black hole's surface area in five dimensions is A+=2π2r3+ and r+ stands for both r+1 and r+2. We also calculate the heat capacity and find that it is positive when the heat bath is placed at a radius r that is equal or less than the photonic orbit, implying in this case thermodynamic stability, and instability otherwise. This means that the small black hole r+1 is unstable and the large one r+2 is stable. A generalized free energy is used to compare the possible thermodynamic phase transitions relative to classical hot flat space which has zero free energy, and we show that it is feasible in certain instances that classical hot flat space transits through r+1 to settle at the stable r+2, with the free energy of the unstable smaller black hole r+1 acting as the potential barrier between the two states. It is also shown that, remarkably, the free energy of the larger r+2 black hole is zero when the cavity radius is equal to the Buchdahl radius. The relation to the instabilities that arise due to perturbations in the path integral in the instanton solution is mentioned. Hot flat space is made of gravitons and it should be treated quantum mechanically rather than classically. Quantum hot flat space has negative free energy and we find the conditions for which the large black hole phase, quantum hot flat space phase, or both are the ground state of the canonical ensemble. The corresponding phase diagram is displayed in a r×T plot showing clearly the three possible phases. Using the density of states ν at a given energy E we also find that the entropy of the large black hole r+2 is S=A+2/4. In addition, we make the connection between the five-dimensional thermodynamics and York's four-dimensional results. [ABSTRACT FROM AUTHOR]

The discovery of new four-dimensional black hole solutions presents a new approach to understand the Gauss-Bonnet gravity in low dimensions. In this paper, we test the Gauss-Bonnet gravity by studying the phase transition and microstructures for the four-dimensional charged anti-de Sitter black hole. In the extended phase space, where the cosmological constant and the Gauss-Bonnet coupling parameter are treated as thermodynamic variables, we find that the thermodynamic first law and the corresponding Smarr formula are satisfied. Both in the canonical ensemble and grand canonical ensemble, we observe the small-large black hole phase transition, which is similar to the case of the van der Walls fluid. This phase transition can also appear in the neutral black hole system. Furthermore, we construct the Ruppeiner geometry, and find that besides the attractive interaction, the repulsive interaction can also dominate among the microstructures for the small black hole with high temperature in a charged or neutral black hole system. This is quite different from the five-dimensional neutral black hole, for which only dominant attractive interaction can be found. The critical behaviors of the normalized scalar curvature are also examined. These results will shed new light into the characteristic property of four-dimensional Gauss-Bonnet gravity. [ABSTRACT FROM AUTHOR]

Considering a canonical ensemble, in which the temperature and charge on a wall of the cavity are fixed, we investigate the thermodynamics of a D-dimensional Gauss-Bonnet black hole in a finite spherical cavity. Moreover, we show that the first law of thermodynamics is still satisfied. We then discuss the phase structure and transition in both five and six dimensions. Specifically, we show that there always exist two regions in the parameter space. In one region, the system possesses one single phase. However, in the other region three phases could coexist and a van der Waals-like phase transition occurs. Finally, we find that there is a fairly close resemblance between the thermodynamic properties and phase structure of a Gauss-Bonnet-Maxwell black hole in a cavity and those in anti-de Sitter space. [ABSTRACT FROM AUTHOR]

We present two new suggestions for density of states (DoS) approaches to finite density lattice QCD. Both proposals are based on the recently developed and successfully tested DoS functional fit approach (FFA) technique, which is a DoS approach for bosonic systems with a complex action problem. The two different implementations of DoS FFA we suggest for QCD make use of different representations of finite density lattice QCD in terms of suitable pseudofermion path integrals. The first proposal is based on a pseudofermion representation of the grand canonical QCD partition sum, while the second is a formulation for the canonical ensemble. We work out the details of the two proposals and discuss the results of exploratory two-dimensional test studies for free fermions at finite density, where exact reference data allow one to verify the final results and intermediate steps. [ABSTRACT FROM AUTHOR]

To obtain deeper understanding of QCD properties at finite temperature, we consider the Fourier decomposition of the grand-canonical partition function based on the canonical ensemble method via the imaginary chemical potential. Expectation values are, then, represented by summation over each canonical sector. We point out that the modified Polyakov loop can play an important role in the canonical ensemble; for example, the Polyakov-loop paradox which is known in the canonical ensemble method can be evaded by considering the quantity. In addition, based on the periodicity issue of the modified Polyakov loop at finite imaginary chemical potential, we can construct the systematic way to compute the dual quark condensate which has strong unclearness in its foundation in the presence of dynamical quarks so far. [ABSTRACT FROM AUTHOR]

Rotation of galactic objects has been seen in the cosmic microwave background (CMB) that could be ascribed to molecular hydrogen clouds with, or without, dust contamination and contamination from other sources. We model the clouds using the canonical ensemble for pure molecular hydrogen, a mixture of hydrogen helium and/or dust, in order to constrain the physical parameters of these clouds. Since the clouds are cold, we justify the use of the canonical ensemble by explicitly calculating the interaction between the hydrogen molecules and the CMB photons and determining the time required for thermal equilibrium to be reached and show that there is enough time for equilibrium to be attained. [ABSTRACT FROM AUTHOR]

The thermodynamic properties of self-gravitating spherical thin matter shells and black holes in d>4 dimensions are studied, extending previous analysis for d=4. The shell joins a Minkowski interior to a Tangherlini exterior, i.e., a Schwarzschild exterior in d dimensions with d≥4. The junction conditions and the first law of thermodynamics enable one to establish that the entropy of the thin shell depends only on its own gravitational radius. Endowing the shell with a power-law temperature equation of state allows one to determine a precise form for the entropy and to perform a thermodynamic stability analysis for the shell. An interesting case is when the shell's temperature has the Hawking form, i.e., it is inversely proportional to the shell's gravitational radius. It is shown in this case that the shell's heat capacity is positive, and thus there is stability, for shells with radii in between their own gravitational radius and the radius of circular photonic orbits, unexpectedly reproducing York's thermodynamic stability criterion for a d=4 black hole in the canonical ensemble. Moreover, the Euler relation for the matter shell is derived, the Bekenstein and holographic entropy bounds are studied, and the large d limit is analyzed. Within this formalism the thermodynamic properties of black holes can be studied, too. Putting the shell at its own gravitational radius, i.e., at the black hole stage, obliges one to choose precisely the Hawking temperature for the shell which in turn yields the Bekenstein-Hawking entropy. The stability analysis implies that the black hole is thermodynamically stable, substantiating that in this configuration our system and York's canonical ensemble black hole are indeed the same system. In addition, within this formalism the Smarr formula for black holes in d dimensions appears naturally and surprisingly. [ABSTRACT FROM AUTHOR]

The action of three-dimensional charged Einstein-dilaton gravity theory has been obtained from that of scalar-tensor modified gravity theory by utilizing the suitable conformal transformations. The field equations of the Einstein-dilaton gravity coupled to the power Maxwell nonlinear electrodynamics have been solved and two new classes of static and spherically symmetric charged dilatonic black holes, as the exact solutions to the coupled scalar, electromagnetic and gravitational field equations, have been obtained. Also, the dilaton potential has been written as the linear combination of two Liouville-type potentials. The black hole conserved charges and thermodynamic quantities have been calculated by utilizing the geometrical and thermodynamical methods, separately. The compatibility of the results obtained from these two alternative approaches confirms the validity of the first law of black hole thermodynamics for both of the new black hole solutions in the Einstein frame. A black hole stability or phase transition analysis has been performed in the context of the canonical ensemble. By calculating the black hole heat capacity, with the black hole charge as a constant, the type one and type two phase transition points have been determined. Also, the ranges of the black hole horizon radii at which the Einstein black holes are thermally stable have been identified for both of the new black hole solutions. Then making use of the inverse conformal transformations, two new classes of the scalar-tensor black holes have been obtained from their Einstein frame counterparts. The thermodynamic properties and thermal stability of the new scalar-tensor black holes have been investigated. It has been found that the new charged black holes have the same thermodynamic behaviors in both of the Einstein and Jordan frames. [ABSTRACT FROM AUTHOR]

We propose a cosmological model, üΛCDM, based on "über gravity," which is a canonical ensemble average of many theories of gravity. In this model, we have a sharp transition from (a purely) ΛCDM era to a phase in which the Ricci scalar is a constant. This transition occurs when the Ricci scalar reaches a critical scale or alternatively a transition redshift, z⊕. We use the observations of baryonic acoustic oscillations and supernovae Ia, as well as the cosmic microwave background data to constrain üΛCDM. This yields H0=70.6+1.1-1.3 km/s/Mpc, Ωm=0.2861±0.0092, and z⊕=0.537+0.277-0.375, providing a marginally better fit with a Akaike information criterion of 0.8. Therefore, üΛCDM can ease the H0 tension, albeit marginally, with one additional free parameter. We also provide a preliminary study of the linear perturbation theory in üΛCDM that points to interesting potential smoking guns in the observations of large scale structure at z

We obtain the Ruppeiner geometry associated with the nonextended state space (Λ constant) of the charged Gauss-Bonnet AdS (GB-AdS) black holes and confirm that the state space Riemannian manifold becomes strongly curved in regions where the black hole system develops strong statistical correlations in the grand canonical ensemble (M and Q fluctuating). We establish the exact proportionality between the state space scalar curvature R and the inverse of the singular free energy near the isolated critical point for the grand canonical ensemble in spacetime dimension d=5, thus hopefully moving a step closer to the agenda of a concrete physical interpretation of R for black holes. On the other hand, we show that while R signals the Davies transition points (which exist in GB-AdS black holes for d≥6) through its divergence, it does not scale as the inverse of the singular free energy there. Furthermore, adapting to the black hole case the ideas developed in [1] in the context of pure fluids, we find that the state space geometry encodes phase coexistence and first order transitions, identifies the asymptotically critical region and even suggests a Widom-line-like crossover regime in the supercritical region for 5-d case. The sign of R appears to imply a significant difference between the microscopic structure of the small and the large black hole branches in d=5. We show that thermodynamic geometry informs the microscopic nature of coexisting thermal GB-AdS and black hole phases near the Hawking-Page phase transition. [ABSTRACT FROM AUTHOR]