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In addition to providing general constraints on probability distributions, fluctuation theorems allow us to infer essential information on the role played by temperature in heat exchange phenomena. In this numerical study, we measure the temperature of an out-of-equilibrium active bath using a fluctuation theorem that relates the fluctuations in the heat exchanged between two baths to their temperatures. Our setup consists of a single particle moving between two wells of a quartic potential accommodating two different baths. The heat exchanged between the two baths is monitored according to two definitions: as the kinetic energy carried by the particle whenever it jumps from one well to the other and as the work performed by the particle on one of the two baths when immersed in it. First, we consider two equilibrium baths at two different temperatures and verify that a fluctuation theorem featuring the baths temperatures holds for both heat definitions. Then, we introduce an additional Gaussian coloured noise in one of the baths, so as to make it effectively an active (out-of-equilibrium) bath. We find that a fluctuation theorem is still satisfied with both heat definitions. Interestingly, in this case the temperature obtained through the fluctuation theorem for the active bath corresponds to the kinetic temperature when considering the first heat definition, while it is larger with the second one. We interpret these results by looking at the particle jump phenomenology. [ABSTRACT FROM AUTHOR]

Recent advancements in information thermodynamics have revealed that information can be directly converted into mechanical work. Specifically, RNA transcription and nanopore sequencing serve as prime examples of this conversion, by reading information from a DNA template. This paper introduces an information thermodynamic model in which these molecular motors can move along the DNA template by converting the information read from the template DNA into their own motion. This process is a stochastic one, characterized by significant fluctuations in forward movement and is described by the Fokker–Planck equation, based on drift velocity and diffusion coefficients. In the current study, it is hypothesized that by utilizing the sequence information of the template DNA as mutual information, the fluctuations can be reduced, thereby biasing the forward movement on DNA and, consequently, reducing reading errors. Further research into the conversion of biological information by molecular motors could unveil new applications, insights, and important findings regarding the characteristics of information processing in biology. [ABSTRACT FROM AUTHOR]

The adaptive and surprising emergent properties of biological materials self-assembled in far-from-equilibrium environments serve as an inspiration for efforts to design nanomaterials. In particular, controlling the conditions of self-assembly can modulate material properties, but there is no systematic understanding of either how to parameterize external control or how controllable a given material can be. Here, we demonstrate that branched actin networks can be encoded with metamaterial properties by dynamically controlling the applied force under which they grow and that the protocols can be selected using multi-task reinforcement learning. These actin networks have tunable responses over a large dynamic range depending on the chosen external protocol, providing a pathway to encoding "memory" within these structures. Interestingly, we obtain a bound that relates the dissipation rate and the rate of "encoding" that gives insight into the constraints on control--both physical and information theoretical. Taken together, these results emphasize the utility and necessity of nonequilibrium control for designing self-assembled nanostructures. [ABSTRACT FROM AUTHOR]

The plastic deformation of almost all solid polymers can be represented by a thermally activated rate process involving the motion of cooperative mobile elements over potential barriers, based on the Eyring activated rate theory. The present study shows that the governing equations for the Eyring rate theory can be completely derived based on the principle of microscopic reversibility in the framework of non-equilibrium dynamics. [ABSTRACT FROM AUTHOR]

The review provides a pedagogical but comprehensive introduction to the foundations of a recently proposed statistical mechanics (μ NEQT) of a stable nonequilibrium thermodynamic body, which may be either isolated or interacting. It is an extension of the well-established equilibrium statistical mechanics by considering microstates m k in an extended state space in which macrostates (obtained by ensemble averaging A ^ ) are uniquely specified so they share many properties of stable equilibrium macrostates. The extension requires an appropriate extended state space, three distinct infinitessimals d α = (d , d e , d i) operating on various quantities q during a process, and the concept of reduction. The mechanical process quantities (no stochasticity) like macrowork are given by A ^ d α q , but the stochastic quantities C ^ α q like macroheat emerge from the commutator C ^ α of d α and A ^ . Under the very common assumptions of quasi-additivity and quasi-independence, exchange microquantities d e q k such as exchange microwork and microheat become nonfluctuating over m k as will be explained, a fact that does not seem to have been appreciated so far in diverse branches of modern statistical thermodynamics (fluctuation theorems, quantum thermodynamics, stochastic thermodynamics, etc.) that all use exchange quantities. In contrast, dq k and d i q k are always fluctuating. There is no analog of the first law for a microstate as the latter is a purely mechanical construct. The second law emerges as a consequence of the stability of the system, and cannot be violated unless stability is abandoned. There is also an important thermodynamic identity  d i Q ≡ d i W   ≥   0 with important physical implications as it generalizes the well-known result of Count Rumford and the Gouy-Stodola theorem of classical thermodynamics. The μ NEQT has far-reaching consequences with new results, and presents a new understanding of thermodynamics even of an isolated system at the microstate level, which has been an unsolved problem. We end the review by applying it to three different problems of fundamental interest. [ABSTRACT FROM AUTHOR]

We establish a fluctuation theorem for an open quantum bipartite system that explicitly manifests the role played by quantum correlation. Generally quantum correlations may substantially modify the universality of classical thermodynamic relations in composite systems. Our fluctuation theorem finds a non-equilibrium parameter of genuinely quantum nature that sheds light on the emerging quantum information thermodynamics. Specifically we show that the statistics of quantum correlation fluctuation obtained in a time-reversed process can provide a useful insight into addressing work and heat in the resulting thermodynamic evolution. We illustrate these quantum thermodynamic relations by two examples of quantum correlated systems. [ABSTRACT FROM AUTHOR]

Novel hidden thermodynamic structures have recently been uncovered during the investigation of nonequilibrium thermodynamics for multiscale stochastic processes. Here we reveal the martingale structure for a general thermodynamic functional of inhomogeneous singularly perturbed diffusion processes under second-order averaging, where a general thermodynamic functional is defined as the logarithmic Radon–Nykodim derivative between the laws of the original process and a comparable process (forward case) or its time reversal (backward case). In the forward case, we prove that the regular and anomalous parts of a thermodynamic functional are orthogonal martingales. In the backward case, while the regular part may not be a martingale, we prove that the anomalous part is still a martingale. With the aid of the martingale structure, we prove the integral fluctuation theorem satisfied by the regular and anomalous parts of a general thermodynamic functional. Further extensions and applications to stochastic thermodynamics are also discussed, including the martingale structure and fluctuation theorems for the regular and anomalous parts of entropy production and housekeeping heat in the absence or presence of odd variables. [ABSTRACT FROM AUTHOR]

Complex systems can convert energy imparted by nonequilibrium forces to regulate how quickly they transition between long-lived states. While such behavior is ubiquitous in natural and synthetic systems, currently there is no general framework to relate the enhancement of a transition rate to the energy dissipated or to bound the enhancement achievable for a given energy expenditure. We employ recent advances in stochastic thermodynamics to build such a framework, which can be used to gain mechanistic insight into transitions far from equilibrium. We show that under general conditions, there is a basic speed limit relating the typical excess heat dissipated throughout a transition and the rate amplification achievable. We illustrate this tradeoff in canonical examples of diffusive barrier crossings in systems driven with autonomous and deterministic external forcing protocols. In both cases, we find that our speed limit tightly constrains the rate enhancement. [ABSTRACT FROM AUTHOR]

We derive the fluctuation theorem for a stochastic and periodically driven system coupled to two reservoirs with the aid of a master equation. We write down the cumulant generating functions for both the current and entropy production in closed compact forms so as to treat the adiabatic and nonadiabatic contributions systematically. We derive the fluctuation theorem by taking into account the time reversal symmetry and the property that the instantaneous currents flowing into the left and the right reservoir are not equal. It is found that the fluctuation–dissipation relation derived from the fluctuation theorem involves an expansion with respect to the time derivative of the affinity. [ABSTRACT FROM AUTHOR]

Spontaneous violations of the Clausius–Duhem (CD) inequality in Couette-type collisional flows of model granular media are studied. Planar systems of monosized circular discs (with disc numbers from 10 to 204, and disc diameters from 0.001 m to 1 m) with frictional-Hookean contacts are simulated under periodic boundary conditions by a molecular dynamics. The scale-dependent homogenization of micropolar media is used to determine the energy balances and mechanical entropy production. The dissipation function exhibits spontaneous negative entropy increments described by the fluctuation theorem. The boundary between violations and non-violations of the CD inequality is mapped in the parameter space, where the probability of such events diminishes with the disc diameter, the disc number and the area fraction increasing. The dissipation function is a random process, tending to Gaussian as the number of discs increases, and possessing non-trivial fractal and anti-persistent Hurst properties. [ABSTRACT FROM AUTHOR]

Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. This energy cascade is modelled by approximating the spectral energy balance with a nonlinear Fokker–Planck equation consistent with accepted phenomenological theories of turbulence. The steady-state contributions of the drift and diffusion in the corresponding Langevin equation, combined with the killing term associated with the dissipation, induce a stochastic energy transfer across wavenumbers. The fluctuation theorem is shown to describe the scale-wise statistics of forward and backward energy transfer and their connection to irreversibility and entropy production. The ensuing turbulence entropy is used to formulate an extended turbulence thermodynamics. [ABSTRACT FROM AUTHOR]

We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such decoupling conditions arise naturally in multifractal analysis, in Gibbs states with hard-core interactions, and in the statistics of repeated quantum measurement processes. We also prove the LDP for the entropy production of pairs of such measures and derive the related Fluctuation Relation. The proofs are based on Ruelle–Lanford functions, and the exposition is essentially self-contained. [ABSTRACT FROM AUTHOR]

Entropy fluctuations with time occur in finite-sized time-evolving dissipative systems. There is a need to comprehend the role of these fluctuations on the fluctuations-averaged entropy generation rate, over a large enough observation time interval. In this non-equilibrium thermodynamic investigation, the Fluctuation Theorem (FT) and Principle of Least Action are re-visited to articulate their implications for dissipative systems. The Principle of Maximum Entropy Production (MaxEP: the entropy generation rate of a dissipative system is maximized by paths of least action) is conceptually identified as the Principle of Least Action for dissipative systems. A Thermodynamic Fusion Theorem that merges the FT and the MaxEP is introduced for addressing the role of fluctuations in entropy production. It identifies "entropy fluctuations" as the "least-action path" for maximizing the time-averaged entropy production in a dissipative system. The validity of this introduced theorem is demonstrated for the case of entropy fluctuations in Rayleigh–Taylor flow instability. [ABSTRACT FROM AUTHOR]

As a central concept in fluid dynamics stability is fundamental in understanding transitions from laminar to turbulent flow. In continuum flows, it is well-established that a transition to turbulence can occur at subcritical Reynolds numbers, in contrast to theoretical predictions. In non-equilibrium molecular dynamics (NEMD), it has been widely observed that at a critical Reynolds number the fluid undergoes an ordering transition from an amorphous phase to a 'string' phase. Using the fluctuation theorem (FT) and the dissipation function, we generalize the classical continuum Reynolds-Orr equation to sheared molecular fluids by ascribing a natural description to the nature of stochastic perturbations, i.e. fluctuations in shear stress. Via the Poincaré inequality, we arrive at a new stability criterion by providing a lower bound on the exponential decay of perturbations, which reduces to the classical continuum result in the limit of infinite system size. We investigate the nature of these velocity perturbations and conditions necessary for growth in the kinetic energy of perturbations. We obtain a fluid dependent estimate for the critical Reynolds number by which one may estimate the critical Reynolds number at which the fluid transitions to the string phase, thus providing a framework for generalizing classical continuum theories to the microscale. [ABSTRACT FROM AUTHOR]

In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality. [ABSTRACT FROM AUTHOR]

We provide a complete derivation of hydrodynamic equations for nonrelativistic systems based on quantum field theories of spinless Schrödeinger fields, assuming that an initial density operator takes a special form of the local Gibbs distribution. The constructed optimized/renormalized perturbation theory for real-time evolution enables us to separately evaluate dissipative and nondissipative parts of constitutive relations. It is shown that the path-integral formula for local thermal equilibrium together with the symmetry properties of the resulting action—the nonrelativistic diffeomorphism and gauge symmetry in the thermally emergent Newton-Cartan geometry—provides a systematic way to derive the nondissipative part of constitutive relations. We further show that dissipative parts are accompanied with the entropy production operator together with two kinds of fluctuation theorems by the use of which we derive the dissipative part of constitutive relations and the second law of thermodynamics. After obtaining the exact expression for constitutive relations, we perform the derivative expansion and derive the first-order hydrodynamic (Navier-Stokes) equation with the Green-Kubo formula for transport coefficients. [ABSTRACT FROM AUTHOR]

The fluctuation theorem is a representative theorem in non-equilibrium statistical physics actively studied in the 1990s. Relating to entropy production in non-equilibrium states, the theorem has been used to estimate the driving power of motor proteins from fluctuation in their motion. In this review, usage of the fluctuation theorem in experiments on motor proteins is illustrated for biologists, especially those who study mechanobiology, in which force measurement is a central issue. We first introduce the application of the fluctuation theorem in measuring the rotary torque of the rotary motor protein F1-ATPase. Next, as an extension of this application, a recent trial estimating the force generated during cargo transport in vivo by the microtubule motors kinesin and dynein is introduced. Elucidation of the physical mechanism of such transport is important, especially for neurons, in which deficits in cargo transport are deeply related to neuronal diseases. Finally, perspectives on the fluctuation theorem as a new technique in the field of neuroscience are discussed. [ABSTRACT FROM AUTHOR]

Fluctuation theorems are a group of exact relations that remain valid irrespective of how far the system has been driven away from equilibrium. Other than having practical applications, like determination of equilibrium free energy change from nonequilibrium processes, they help in our understanding of the second law and the emergence of irreversibility from time-reversible equations of motion at microscopic level. A vast number of such theorems have been proposed in literature, ranging from Hamiltonian to stochastic systems, from systems in steady state to those in transient regime, and for both open and closed quantum systems. In this article, we discuss about a few such relations, when the system evolves under Hamiltonian dynamics. [ABSTRACT FROM AUTHOR]

In this work, we discussed the stochastic thermodynamics of mesoscopic electron transfer reactions between ions and electrodes. With a relationship between the reaction rate constant and the electrode potential, we find that the heat dissipation βq equals to the dynamic irreversibility of the reaction system minus an internal entropy change term. The total entropy change Δst is defined as the summation of the system entropy change Δs and the heat dissipation βq such that Δst=Δs+βq. Even though the heat dissipation depends linearly on the electrode potential, the total entropy change is found to satisfy the fluctuation theorem -Δst>=1, and hence a second law-like inequality reads <Δst>≥0. Our study provides a practical methodology for the stochastic thermodynamics of electrochemical reactions, which may find applications in biochemical and electrochemical reaction systems. [ABSTRACT FROM AUTHOR]

The steady-state work fluctuations for an overdamped Brownian particle driven by an external stochastic force are analyzed by using the Langevin approach. The first two moments of the work distribution are given analytically, both are proportional to the time duration of the work injection. The first two moments determine a unique Gaussian function, and the deviations of the probability density functions (PDFs) of work from the Gaussian functions are measured. The tails of the PDFs are shown to approximate the Gaussian functions. In the limit of weak external force and large time interval, the PDF can be approximated by the Gaussian form and the steady-state fluctuation theorem is held. [ABSTRACT FROM AUTHOR]

The analysis of cellular signaling cascades based on information thermodynamics has recently developed considerably. A signaling cascade may be considered a binary code system consisting of two types of signaling molecules that carry biological information, phosphorylated active, and non-phosphorylated inactive forms. This study aims to evaluate the signal transduction step in cascades from the viewpoint of changes in mixing entropy. An increase in active forms may induce biological signal transduction through a mixing entropy change, which induces a chemical potential current in the signaling cascade. We applied the fluctuation theorem to calculate the chemical potential current and found that the average entropy production current is independent of the step in the whole cascade. As a result, the entropy current carrying signal transduction is defined by the entropy current mobility. [ABSTRACT FROM AUTHOR]

We formulate a box model of coupled ocean-atmosphere to examine the differential fields interactive with the thermohaline circulation (THC) and their response to global warming. We discern a robust convective bound on the atmospheric heat transport, which would divide the climate regime into warm and cold branches; but unlike the saline mode of previous box models, the cold state, if allowed, has the same-signed-though weaker-density contrast and THC as the present climate, which may explain its emergence from coupled general circulation models. We underscore the nondeterminacy of the THC due to random eddy shedding and apply the fluctuation theorem to constrain the shedding rate, thus closing the problem. The derivation reveals an ocean propelled toward the maximum entropy production (MEP) on millennial timescale (termed 'MEP-adjustment'), the long timescale arising from the compounding effect of microscopic fluctuations in the shedding rate and their slight probability bias. Global warming may induce hysteresis between the two branches, like that seen in GCMs, but the cold transition is far more sensitive to the moistening than the heating effects as the latter would be countered by the hydrological feedback. The uni- or bi-modality of the current state-hence whether the THC may recover after the cold transition-depends on the global-mean convective flux and may not be easily assessed due to its observed uncertainty. [ABSTRACT FROM AUTHOR]

Close to equilibrium, the exchange of particles and heat between macroscopic systems at different temperatures and different chemical potentials is known to be governed by a matrix of transport coefficients which are positive and symmetric. We investigate the amounts of heat and particles that are exchanged between two small quantum systems within a given time, and find them characterized by a transport matrix which neither needs to be symmetric nor positive. At larger times even spontaneous transport can be observed in the total absence of temperature and chemical potential differences provided that the two systems are different in size. All these deviations from standard transport behavior can be attributed to the fact that work is done on the system in the processes contacting and separating those parts of the system that initially possess different temperatures and chemical potentials. The standard transport properties are recovered for vanishing work and also in the limit of large systems and sufficiently large contact times. The general results are illustrated by an example. [ABSTRACT FROM AUTHOR]

Maintained by environmental fluxes, biological systems are thermodynamic processes that operate far from equilibrium without detailed-balanced dynamics. Yet, they often exhibit well defined nonequilibrium steady states (NESSs). More importantly, critical thermodynamic functionality arises directly from transitions among their NESSs, driven by environmental switching. Here, we identify the constraints on excess heat and dissipated work necessary to control a system that is kept far from equilibrium by background, uncontrolled 'housekeeping' forces. We do this by extending the Crooks fluctuation theorem to transitions among NESSs, without invoking an unphysical dual dynamics. This and corresponding integral fluctuation theorems determine how much work must be expended when controlling systems maintained far from equilibrium. This generalizes thermodynamic feedback control theory, showing that Maxwellian Demons can leverage mesoscopic-state information to take advantage of the excess energetics in NESS transitions. We also generalize an approach recently used to determine the work dissipated when driving between functionally relevant configurations of an active energy-consuming complex system. Altogether, these results highlight universal thermodynamic laws that apply to the accessible degrees of freedom within the effective dynamic at any emergent level of hierarchical organization. By way of illustration, we analyze a voltage-gated sodium ion channel whose molecular conformational dynamics play a critical functional role in propagating action potentials in mammalian neuronal membranes. [ABSTRACT FROM AUTHOR]

Stochastic motion of macrospins is similar to driven diffusion of Brownian particles on the surface of a sphere. One crucial difference is in how the micro-states transform under time reversal. This dictates the form of stochastic entropy production (sEP). An excess sEP in the reservoir, in addition to a Clausius term, may appear depending on the interpretation of stochastic trajectory, thereby, precluding such analysis without a detailed knowledge of the governing dynamics. To show this, we derive expressions of sEP using Fokker-Planck equation, and the ratio of probability distributions of time-forward and time-reversed trajectories. We calculate probability distributions of sEP using numerical simulations, and obtain good agreement with the detailed fluctuation theorem. Within adiabatic approximation, analytic form for the distribution function is also derived. [ABSTRACT FROM AUTHOR]

Based on the fluctuation theorem of a small engine, we present a description of the stochastic dynamics of a mesoscopic system. We apply it to the problem of the escape of a particle from a metastable state subjected to a fluctuating nonconservative force, which is beyond the description of the fluctuation-dissipation theorem. As an example, we consider a reversal of a small magnetic moment by fluctuating spin-torque. The joint probability distribution of input heat and output work is derived from the full-counting statistics under adiabatic pumping. We predict a threshold voltage above which the spin-torque shot noise induces probabilistic switching events, and below which such events are blocked. [ABSTRACT FROM AUTHOR]

We survey new extensions of continuum mechanics incorporating spontaneous violations of the Second Law (SL), which involve the viscous flow and heat conduction. First, following an account of the Fluctuation Theorem (FT) of statistical mechanics that generalizes the SL, the irreversible entropy is shown to evolve as a submartingale. Next, a stochastic thermomechanics is formulated consistent with the FT, which, according to a revision of classical axioms of continuum mechanics, must be set up on random fields. This development leads to a reformulation of thermoviscous fluids and inelastic solids. These two unconventional constitutive behaviors may jointly occur in nano-poromechanics. [ABSTRACT FROM AUTHOR]

We consider a model of N interacting two-colour Friedman urns. The interaction model considered is such that the reinforcement of each urn depends on the fraction of balls of a particular colour in that urn as well as the overall fraction of balls of that colour in all the urns combined together. We show that the urns synchronize almost surely and that the fraction of balls of each colour converges to the deterministic limit of one-half, which matches with the limit known for a single Friedman urn. Furthermore, we use the notion of stable convergence to obtain limit theorems for fluctuations around the synchronization limit. [ABSTRACT FROM AUTHOR]

We establish quantum thermodynamics for open quantum systems weakly coupled to their reservoirs when the system exhibits degeneracies. The first and second law of thermodynamics are derived, as well as a finite-time fluctuation theorem for mechanical work and energy and matter currents. Using a double quantum dot junction model, local eigenbasis coherences are shown to play a crucial role on thermodynamics and on the electron counting statistics. [ABSTRACT FROM AUTHOR]

In this note, we consider the fluctuation theorem for $$X_{f_n}^{(n)}:=\sum _{i=1}^n f(\lambda _i)I(\lambda _i\ge \theta _n)$$ , where $$\lambda _i, i=1,\ldots ,n$$ are eigenvalues from a Wigner matrix and $$\theta _n\rightarrow 2^-$$ . We prove that in the edge case $$X_{f_n}^{(n)}$$ behaves like the counting function of Wigner matrix. Our results can be viewed as a complement of Bao et al. (J Stat Phys 150(1):88-129, 2013). [ABSTRACT FROM AUTHOR]

Spontaneous, random violations of the second law become relevant as the length and/or timescales become very small. Modern statistical physics tells us that the second law then needs to be replaced by the fluctuation theorem and, mathematically, the irreversible entropy evolves as a submartingale. This is illustrated on the Couette flow of a molecular fluid. On the continuum level, such phenomena lead to a framework of thermomechanics relying on stochastic (rather than deterministic) functionals of energy and entropy, which are applied in heat diffusion and thermoelasticity settings. Counterintuitive thermomechanical behaviors are also discussed in (1) the evolution of acceleration wavefronts of nanoscale thickness and (2) the fluid mechanics which has to enter a permeability model of a poroelastic medium with nanoscale pores. [ABSTRACT FROM PUBLISHER]

We consider two different methods of calculating the relevant average for the non-equilibrium partition identity (NPI), i.e., which result in two different values. At best only one of these will accurately correspond to what is observed. In order to better understand the two outcomes we carry out a detailed error analysis. This analysis is difficult due to the importance of extremely rare events in forming the average, resulting in the necessity to go beyond linear approximations for the error estimates. We begin by analysing the error in the fluctuation relation, and build upon this to estimate the errors in the NPI average. At short durations the full ensemble average always gives the observed average (i.e. the NPI holds). However, at very long durations, given a fixed amount of sampling, the observed average is predicted by treating the probability distribution as a Dirac-delta function. At intermediate times, neither corresponds to the observed average. This has profound implications for non-equilibrium work relations, as first introduced by Jarzynski. [ABSTRACT FROM AUTHOR]

The violations of the second law are relevant as the length and/or time scales become very small. The second law then needs to be replaced by the fluctuation theorem and mathematically, the irreversible entropy is a submartingale. First, we discuss the consequences of these results for the axioms of continuum mechanics, arguing in favor of a framework relying on stochastic functionals of energy and entropy. We next determine a Lyapunov function for diffusion-type problems governed by stochastic rather than deterministic functionals of internal energy and entropy, where the random field coefficients of diffusion are not required to satisfy the positive definiteness everywhere. Next, a formulation of micropolar fluid mechanics is developed, accounting for the lack of symmetry of stress tensor on molecular scales. This framework is then applied to employed to show that spontaneous random fluctuations of the microrotation field will arise in Couette-and Poiseuille-type flows in the absence of random (turbulence-like) fluctuations of the classical velocity field. Finally, while the permeability is classically modeled by the Darcy law or its modifications, besides considering the violations of the second law, one also needs to account for the spatial randomness of the channel network, implying a modification of the hierarchy of scale-dependent bounds on the macroscopic property of the network. [ABSTRACT FROM AUTHOR]

Directly observing protein folding in real time using atomic force microscopy (AFM) is challenging. Here the use of AFM to directly monitor the folding of an α/β protein, NuG2, by using low-drift AFM cantilevers is demonstrated. At slow pulling speeds (<50 nm s−1), the refolding of NuG2 can be clearly observed. Lowering the pulling speed reduces the difference between the unfolding and refolding forces, bringing the non-equilibrium unfolding-refolding reactions towards equilibrium. At very low pulling speeds (ca. 2 nm s−1), unfolding and refolding were observed to occur in near equilibrium. Based on the Crooks fluctuation theorem, we then measured the equilibrium free energy change between folded and unfolded states of NuG2. The improved long-term stability of AFM achieved using gold-free cantilevers allows folding-unfolding reactions of α/β proteins to be directly monitored near equilibrium, opening the avenue towards probing the folding reactions of other mechanically important α/β and all-β elastomeric proteins. [ABSTRACT FROM AUTHOR]

Systems of hexatic smectic B liquid crystal are investigated by constant-pressure and constant-temperature molecular dynamics simulations. By using a symplectic integrator designed for soft-matter under a condition where the fluctuation of the system is large, spontaneous transfer among the metastable states is observed. By analyzing the transfer in both directions, distributions of work values corresponding to the forward and reverse processes are obtained. [ABSTRACT FROM AUTHOR]

The process of gene regulation is comprised of intrinsically random events resulting in large cell-to-cell variability in mRNA and protein numbers. With gene expression being the central dogma of molecular biology, it is essential to understand the origin and role of these fluctuations. An intriguing observation is that the number of mRNA present in a cell are not only random and small but also that they are produced in bursts. The gene switches between an active and an inactive state, and the active gene transcribes mRNA in bursts. Transcriptional noise being bursty, so are the number of proteins and the subsequent gene expression levels. It is natural to ask the question: what is the reason for the bursty mRNA dynamics? And can the bursty dynamics be shown to be entropically favorable by studying the reaction kinetics underlying the gene regulation mechanism? The dynamics being an out-of-equilibrium process, the fluctuation theorem for entropy production in the reversible reaction channel is discussed. We compute the entropy production rate for varying degrees of burstiness. We find that the reaction parameters that maximize the burstiness simultaneously maximize the entropy production rate. [ABSTRACT FROM AUTHOR]

The results established in contemporary statistical physics indicating that, on very small space and time scales, the entropy production rate may be negative, motivate a generalization of continuum mechanics. On account of the fluctuation theorem, it is recognized that the evolution of entropy at a material point is stochastically (not deterministically) conditioned by the past history, with an increasing trend of average entropy production. Hence, the axiom of Clausius- Duhem inequality is replaced by a submartingale model, which, by the Doob decomposition theorem, allows classification of thermomechanical processes into four types depending on whether they are conservative or not and/or conventional continuum mechanical or not. Stochastic generalizations of thermomechanics are given in the vein of either thermodynamic orthogonality or primitive thermodynamics, with explicit models formulated for Newtonian fluids with, respectively, parabolic or hyperbolic heat conduction. Several random field models of the martingale component, possibly including spatial fractal and Hurst effects, are proposed. The violations of the second law are relevant in those situations in continuum mechanics where very small spatial and temporal scales are involved. As an example, we study an acceleration wavefront of nanoscale thickness which randomly encounters regions in the medium characterized by a negative viscosity coefficient. [ABSTRACT FROM AUTHOR]

We construct different equivalent non-equilibrium statistical ensembles in a simple yet instructive $$N$$ -degrees of freedom model of atmospheric turbulence, introduced by Lorenz in 1996. The vector field can be decomposed into an energy-conserving, time-reversible part, plus a non-time reversible part, including forcing and dissipation. We construct a modified version of the model where viscosity varies with time, in such a way that energy is conserved, and the resulting dynamics is fully time-reversible. For each value of the forcing, the statistical properties of the irreversible and reversible model are in excellent agreement, if in the latter the energy is kept constant at a value equal to the time-average realized with the irreversible model. In particular, the average contraction rate of the phase space of the time-reversible model agrees with that of the irreversible model, where instead it is constant by construction. We also show that the phase space contraction rate obeys the fluctuation relation, and we relate its finite time corrections to the characteristic time scales of the system. A local version of the fluctuation relation is explored and successfully checked. The equivalence between the two non-equilibrium ensembles extends to dynamical properties such as the Lyapunov exponents, which are shown to obey to a good degree of approximation a pairing rule. These results have relevance in motivating the importance of the chaotic hypothesis. in explaining that we have the freedom to model non-equilibrium systems using different but equivalent approaches, and, in particular, that using a model of a fluid where viscosity is kept constant is just one option, and not necessarily the only option, for describing accurately its statistical and dynamical properties. [ABSTRACT FROM AUTHOR]

Vacuolar-type H-pumping ATPases (V-ATPases) perform remarkably diverse functions in eukaryotic organisms. They are present in the membranes of many organelles and regulate the pH of several intracellular compartments. A family of V-ATPases is also present in the plasma membranes of some bacteria. Such V-ATPases function as ATP-synthases. Each V-ATPase is composed of a water-soluble domain (V) and a membrane-embedded domain (V). The ATP-driven rotary unit, V $$_1$$ , is composed of A, B, D, and F subunits. The rotary shaft (the DF subcomplex) rotates in the central cavity of the AB-ring (the catalytic hexamer ring). The D-subunit, which has a coiled-coil domain, penetrates into the ring, while the F-subunit is a globular-shaped domain protruding from the ring. The minimal ATP-driven rotary unit of V $$_1$$ is comprised of the ABD subunits, and we therefore investigated how the absence of the globular-shaped F-subunit affects the rotary torque generation of V $$_1$$ . Using a single-molecule technique, we observed the motion of the rotary motors. To obtain the torque values, we then analyzed the measured motion trajectories based on the fluctuation theorem, which states that the law of entropy production in non-equilibrium conditions and has been suggested as a novel and effective method for measuring torque. The measured torque of ABD was half that of the wild-type V, and full torque was recovered in the mutant V, in which the F-subunit was genetically fused with the D-subunit, indicating that the globular-shaped F-subunit reinforces torque generation in V. [ABSTRACT FROM AUTHOR]

It is now well established that most if not all enzymatic proteins display a slow stochastic dynamics of transitions between a variety of conformational substates composing their native state. A hypothesis is stated that the protein conformational transition networks, as just as higher-level biological networks, the protein interaction network, and the metabolic network, have evolved in the process of self-organized criticality. Here, the criticality means that all the three classes of networks are scale-free and, moreover, display a transition from the fractal organization on a small length-scale to the small-world organization on the large length-scale. Good mathematical models of such networks are stochastic critical branching trees extended by long-range shortcuts. Biological molecular machines are proteins that operate under isothermal conditions and hence are referred to as free energy transducers. They can be formally considered as enzymes that simultaneously catalyze two chemical reactions: the free energy-donating (input) reaction and the free energy-accepting (output) one. The far-from-equilibrium degree of coupling between the output and the input reaction fluxes have been studied both theoretically and by means of the Monte Carlo simulations on model networks. For single input and output gates the degree of coupling cannot exceed unity. Study simulations of random walks on model networks involving more extended gates indicate that the case of the degree of coupling value higher than one is realized on the mentioned above critical branching trees extended by long-range shortcuts. [ABSTRACT FROM AUTHOR]

Some critical trends in information theory, its role in living systems and utilization in fluctuation theory are discussed. The mutual information of thermodynamic coupling is incorporated into the generalized fluctuation theorem by using information theory and nonequilibrium thermodynamics. Thermodynamically coupled dissipative structures in living systems are capable of degrading more energy, and processing complex information through developmental and environmental constraints. The generalized fluctuation theorem can quantify the hysteresis observed in the amount of the irreversible work in nonequilibrium regimes in the presence of information and thermodynamic coupling. [ABSTRACT FROM AUTHOR]

It is now well established that most if not all enzymatic proteins display a slow stochastic dynamics of transitions between a variety of conformational substates composing their native state. A hypothesis is stated that the protein conformational transition networks, as just as higher-level biological networks, the protein interaction network, and the metabolic network, have evolved in the process of self-organized criticality. Here, the criticality means that all the three classes of networks are scale-free and, moreover, display a transition from the fractal organization on a small length-scale to the small-world organization on the large length-scale. Good mathematical models of such networks are stochastic critical branching trees extended by long-range shortcuts. Biological molecular machines are proteins that operate under isothermal conditions and hence are referred to as free energy transducers. They can be formally considered as enzymes that simultaneously catalyze two chemical reactions: the free energy-donating (input) reaction and the free energy-accepting (output) one. The far-from-equilibrium degree of coupling between the output and the input reaction fluxes have been studied both theoretically and by means of the Monte Carlo simulations on model networks. For single input and output gates the degree of coupling cannot exceed unity. Study simulations of random walks on model networks involving more extended gates indicate that the case of the degree of coupling value higher than one is realized on the mentioned above critical branching trees extended by long-range shortcuts. [ABSTRACT FROM AUTHOR]

Some critical trends in information theory, its role in living systems and utilization in fluctuation theory are discussed. The mutual information of thermodynamic coupling is incorporated into the generalized fluctuation theorem by using information theory and nonequilibrium thermodynamics. Thermodynamically coupled dissipative structures in living systems are capable of degrading more energy, and processing complex information through developmental and environmental constraints. The generalized fluctuation theorem can quantify the hysteresis observed in the amount of the irreversible work in nonequilibrium regimes in the presence of information and thermodynamic coupling. [ABSTRACT FROM AUTHOR]

We study a class of finite dimensional quantum dynamical semigroups $\{\mathrm {e}^{t\mathcal{L}}\}_{t\geq0}$ whose generators $\mathcal{L}$ are sums of Lindbladians satisfying the detailed balance condition. Such semigroups arise in the weak coupling (van Hove) limit of Hamiltonian dynamical systems describing open quantum systems out of equilibrium. We prove a general entropic fluctuation theorem for this class of semigroups by relating the cumulant generating function of entropy transport to the spectrum of a family of deformations of the generator ${\mathcal{L}}$. We show that, besides the celebrated Evans-Searles symmetry, this cumulant generating function also satisfies the translation symmetry recently discovered by Andrieux et al., and that in the linear regime near equilibrium these two symmetries yield Kubo's and Onsager's linear response relations. [ABSTRACT FROM AUTHOR]

As shown by Jarzynski, free energy differences between equilibrium states can be expressed in terms of the statistics of work carried out on a system during non-equilibrium transformations. This exact result, as well as the related Crooks fluctuation theorem, provide the basis for the computation of free energy differences from fast switching molecular dynamics simulations, in which an external parameter is changed at a finite rate, driving the system away from equilibrium. In this article, we first briefly review the Jarzynski identity and the Crooks fluctuation theorem and then survey various algorithms building on these relations. We pay particular attention to the statistical efficiency of these methods and discuss practical issues arising in their implementation and the analysis of the results. [ABSTRACT FROM AUTHOR]

When systems are far from equilibrium, the temperature, the entropy and the thermodynamic entropy production are not defined and the Gibbs entropy does not provide useful information about the physical properties of a system. Furthermore, far from equilibrium, or if the dissipative field changes in time, the spontaneous entropy production of linear irreversible thermodynamics becomes irrelevant. In 2000 we introduced a definition for the dissipation function and showed that for systems of arbitrary size, arbitrarily near or far from equilibrium, the time integral of the ensemble average of this quantity can never decrease. In the low-field limit, its ensemble average becomes equal to the spontaneous entropy production of linear irreversible thermodynamics. We discuss how these quantities are related and why one should use dissipation rather than entropy or entropy production for non-equilibrium systems. [ABSTRACT FROM PUBLISHER]

A grand challenge in the field of artificial life is to find a general theory of emergent self-organizing systems. In swarm systems most of the observed complexity is based on motion of simple entities. Similarly, statistical mechanics focuses on collective properties induced by the motion of many interacting particles. In this article we apply methods from statistical mechanics to swarm systems. We try to explain the emergent behavior of a simulated swarm by applying methods based on the fluctuation theorem. Empirical results indicate that swarms are able to produce negative entropy within an isolated subsystem due to frozen accidents. Individuals of a swarm are able to locally detect fluctuations of the global entropy measure and store them, if they are negative entropy productions. By accumulating these stored fluctuations over time the swarm as a whole is producing negative entropy and the system ends up in an ordered state. We claim that this indicates the existence of an inverted fluctuation theorem for emergent self-organizing dissipative systems. This approach bears the potential of general applicability. [ABSTRACT FROM AUTHOR]