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Tracking the Brownian motion of aerosol particles as they settle in air allows a mass measurement. The particle typically falls downward at its terminal settling velocity; however, the particle occasionally will be displaced upwards due to Brownian fluctuations. The number of occurrences of upward and downward fluctuations is compared, using the formula for the work fluctuation theorem, to yield the mass. This method can be applied to either a single particle or a collection of particles. The advantages of this method include no required information about the size, shape, or density of the particle. Details of the analysis method are presented and illustrated with experimental data.

General relations for nonequilibrium spin transport at a magnetic junction between a normal metal and a ferromagnetic insulator are derived from the quantum fluctuation theorem. They include the extended Onsager relations between the spin conductance and the spin-current noise that hold for nonequilibrium states driven by an external current. These relations, that are valid for a general setup of spin Hall magnetoresistance, provide a comprehensive viewpoint for understanding of unidirectional spin Hall magnetoresistance in insulating ferromagnetic junctions., Comment: 8 pages, 1 figure

In this work we explore the validity of the transient work fluctuation theorem as well as the Jarzynski equality. In the case of a Brownian particle dragged through a fluid by an optical trap, the fluid plays the role of a non-Markovian heat bath characterized by an specific Ornstein–Uhlenbeck friction memory kernel. To achieve our goal, we used an alternative method which transformed the generalized Langevin equation into an equivalent third-order non-Markovian Langevin equation. By means of the exact analytical solution of this Langevin equation, we calculated the statistics of thermodynamic work which established the Crooks relation, and then the Jarzynski equality came immediately. The fluctuation theorems are applicable to small systems where energy fluctuations with respect to the average behavior are big enough to be measured. The examples of such a class of systems are found inside living organisms.

Using Non-equilibrium Molecular Dynamics (NEMD) simulations, we study the statistical properties of an atomic fluid undergoing planar Couette flow, in which particles interact via a Lennard-Jones potential. We draw a connection between local density contrast and temporal fluctuations in the shear stress, which arise naturally through the equivalence between the dissipation function and entropy production according to the fluctuation theorem. We focus on the shear stress and the spatio-temporal density fluctuations and study the autocorrelations and spectral densities of the shear stress. The bispectral density of the shear stress is used to measure the degree of departure from a Gaussian model and the degree of nonlinearity induced in the system owing to the applied strain rate. More evidence is provided by the probability density function of the shear stress. We use the Information Theory to account for the departure from Gaussian statistics and to develop a more general probability distribution function that captures this broad range of effects. By accounting for negative shear stress increments, we show how this distribution preserves the violations of the Second Law of Thermodynamics observed in planar Couette flow of atomic fluids, and also how it captures the non-Gaussian nature of the system by allowing for non-zero higher moments. We also demonstrate how the temperature affects the band-width of the shear-stress and how the density affects its Power Spectral Density, thus determining the conditions under which the shear-stress acts is a narrow-band or wide-band random process. We show that changes in the statistical characteristics of the parameters of interest occur at a critical strain rate at which an ordering transition occurs in the fluid causing shear thinning and affecting its stability. A critical strain rate of this kind is also predicted by the Loose–Hess stability criterion.

The McLennan-Zubarev steady state distribution is studied in the connection with fluctuation theorems. We derive the McLennan-Zubarev steady state distribution from the nonequilibrium detailed balance relation. Then, considering the cumulant function or cumulant functional, two fluctuation theorems for entropy and for currents are proved. Using the fluctuation theorem for currents, the current is expanded in terms of thermodynamic forces. In the lowest order of the thermodynamic force, we find that the transport coefficient satisfies the Onsager's reciprocal relation. In the next order, we derived the correction term to the Green-Kubo formula., Comment: 19 pages, 1 figure. Accepted for publication in Physica A

The validity of the fluctuation theorems for total entropy production of a colloidal particle embedded in a non-Markovian heat bath driven by a time-dependent force in a harmonic potential is probed here. The dynamics of the system is modeled by the generalized Langevin equation with colored noise. The distribution function of the total entropy production is calculated and the detailed fluctuation theorem contains a renormalized temperature term which arises due to the non-Markovian characteristics of the thermal bath.

A continuum plasticity model for metals is presented from considerations of non-equilibrium thermodynamics. Of specific interest is the application of a fluctuation relation that subsumes the second law of thermodynamics en route to deriving the evolution equations for the internal state variables. The modelling itself is accomplished in a two-temperature framework that appears naturally by considering the thermodynamic system to be composed of two weakly interacting subsystems, viz. a kinetic vibrational subsystem corresponding to the atomic lattice vibrations and a configurational subsystem of the slower degrees of freedom describing the motion of defects in a plastically deforming metal. An apparently physical nature of the present model derives upon considering the dislocation density, which characterizes the configurational subsystem, as a state variable. Unlike the usual constitutive modelling aided by the second law of thermodynamics that merely provides a guideline to select the admissible (though possibly non-unique) processes, the present formalism strictly determines the process or the evolution equations for the thermodynamic states while including the effect of fluctuations. The continuum model accommodates finite deformation and describes plastic deformation in a yield-free setup. The theory here is essentially limited to face-centered cubic metals modelled with a single dislocation density as the internal variable. Limited numerical simulations are presented with validation against relevant experimental data. (C) 2016 Elsevier Ltd. All rights reserved.

The mechanisms of the strong inward rectification in inward rectifier K(+) (Kir) channels are controversial because the drop in electrical potential due to the movement of the blocker and coupling ions is insufficient to explain the steep voltage-dependent block near the equilibrium potential. Here, we study the "driving force"-dependent block in Kir channels with a novel approach incorporating concepts from the non-equilibrium thermodynamics of small systems, and computer kinetic simulations based on the experimental data of internal Ba(2+) block on Kir2.1 channels. The steep exponential increase in the apparent binding rate near the equilibrium potential is explained, when the encounter frequency is construed as the likelihood of transfer events down or against the electrochemical potential gradient. The exponent of flux ratio, nf=2.62, implies that the blockage of the internal blocker may be coupled with the outward transport of 2 to 3K(+) ions. The flux-coupled block in the single-file multi-ion pore can be demonstrated by the concentration gradient alone, as well as when the driving force is the electrochemical potential difference across the membrane.

A nonequilibrium fluctuation theorem is established for a colloidal particle driven by an external force within the hydrodynamic theory of Brownian motion, describing hydrodynamic memory effects such as the t^(-3/2) power-law decay of the velocity autocorrelation function. The generalized Langevin equation is obtained for the general case of slip boundary conditions between the particle and the fluid. The Gaussian probability distributions for the particle to evolve in position-velocity space are deduced. It is proved that the joint probability distributions of forward and time-reversed paths have a ratio depending only on the work performed by the external force and the fluid temperature, in spite of the nonMarkovian character of the generalized Langevin process., Dedicated to the memory of Christian Van den Broeck

Cytoplasmic dynein exhibits a directional processive movement on microtubule filaments and is known to move in steps of varying length based on the number of ATP molecules bound to it and the load that it carries. It is experimentally observed that dynein takes occasional backward steps and the frequency of such backward steps increases as the load approaches the stall force. Using a stochastic process model, we investigate the bidirectional movement of single head of a dynein motor. The probability for backward step is implemented based on fluctuation theorem of non-equilibrium statistical mechanics. We find that the movement of dynein motor is characterized with negative velocity implying backward motion beyond stall force. We observe that the motor moves backward for super stall forces by hydrolyzing the ATP exactly the same way as it does while moving forward for sub-stall forces. Movement of dynein is also simulated using a kinetic Monte Carlo method and the simulated velocities are in good agreement with velocities obtained using a stochastic rate equation model.

We develop a theoretical framework for the stochastic thermodynamics of reactive systems. We show that the transition probabilities per unit time of reactive events must satisfy specific constraints, in order for stochastic approaches to lead to physically meaningful results in the macroscopic limit. We discuss how these constraints affect the properties of stochastic fluxes and forces, and entropy production. We also see how they can be used to derive various expressions of fluctuation theorems.

We discuss multiplicity fluctuation caused by noises during hydrodynamic evolution of the quark-gluon fluid created in high-energy nuclear collisions., Comment: 4 pages, 1 figure, proceedings of the XXIV Quark Matter conference, May 19-24 2014, Darmstadt (Germany)

The work fluctuations of a quantum Brownian particle driven by an external force in a general nonergodic heat bath are studied under a general initial state. The exact analytical expression of the work probability distribution function is derived. Results show the existence of a quantum asymptotic fluctuation theorem, which is in general not a direct generalization of its classical counterpart. The form of this theorem is dependent on the structure of the heat bath and the specified initial condition.

We derive the integral fluctuation theorem around a nonequilibrium stationary state for frictionless and soft core granular particles under an external vibration achieved by a balance between an external vibration and inelastic collisions. We also discuss the connection between the integral fluctuation theorem and the generalized Green-Kubo formula., 15 pages, no figures to be published in Comptes rendus - M\'ecanique as Proceedings of EuroMech2012 at Graz, Austria

We investigate non-equilibrium nature of fluctuations of black hole horizons by applying the fluctuation theorems and the Jarzynski equality developed in the non-equilibrium statistical physics. These theorems applied to space–times with black hole horizons lead to the generalized second law of thermodynamics. It is also suggested that the second law should be violated microscopically so as to satisfy the Jarzynski equality.

The Speck–Seifert equality and the Hatano–Sasa equality are known to be bases to construct stationary state thermodynamics. The well known nonequilibrium relations, the Jarzynski equality and the fluctuation theorem, share the mathematical structure with the above equalities. This hidden common property motivates us to extend the Jarzynski equality to a relation applicable in the generalized dynamical system. As a result, we find several equalities which are able to be established in this generalized system described by the Langevin equation. These results easily reproduce the Speck–Seifert equality and the Hatano–Sasa equality. We hope that our formulation gives a new insight on nonequilibrium statistical physics.

Non-thermal Brownian motion of a particle for soft-mode turbulence (SMT) in the electroconvection of a nematic liquid crystal has been experimentally investigated to clarify the statistical and thermodynamical aspects of SMT, using the Lagrangian picture in hydrodynamics. The effective temperature for SMT is obtained in two different ways based on the Einstein relation and the fluctuation theorem from the diffusion due to non-thermal particle fluctuations. The temperatures from the two methods agree well and exhibit a high value of 106 K. They depend on the coarse-graining time, which reflects the anomalous properties of the macroscopic fluctuations for the SMT.

We generalize the second law of thermodynamics in its maximum work formulation for a nonequilibrium initial distribution. It is found that in an isothermal process, the Boltzmann relative entropy (H-function) is not just a Lyapunov function but also tells us the maximum work that may be gained from a nonequilibrium initial state. The generalized second law also gives a fundamental relation between work and information. It is valid even for a small Hamiltonian system not in contact with a heat reservoir but with an effective temperature determined by the isentropic condition. Our relation can be tested in the Szilard engine, which will be realized in the laboratory.

We study the fluctuation theorem formulated in terms of the currents present in a Hamiltonian system with coupled mass and energy transport. To drive the system out of equilibrium, we assume it to be connected to two ideal thermodynamical baths. The fluctuation symmetry is, thus, expressed in terms of the joint probability distribution of energy and particle currents in the system. This relation is verified numerically for the stationary state in the Spinning Lorentz Gas (SLG), driven out of equilibrium by temperature and/or chemical potential differences between the baths, as well as in the presence of an applied field.

We consider the statistical irreversibility and its compatibility with the reversible dynamics. The role played by the observation is analyzed in detail. It makes our previous proof for the second law of thermodynamics clearer. On this basis, we emphasize the importance and wide applicability for the second law of thermodynamics. A new form of physics with this law being substituted by the principle of information conservation is suggested. By the way, we also solve the paradox of Schr\"odinger cat, and show that the universe will not go to the so-called heat death spontaneously., Comment: 7 pages, 9 figure

The negentropy proposed first by Schroedinger is re-examined, and its conceptual and mathematical definitions are introduced. This re-definition of negentropy integrates Schroedinger’s intention of its introduction, and the subsequent diverse notions in literature. This negentropy is further corroborated by its ability to state the two exact thermodynamic principles: negentropy principle for dynamic order existence and principle of maximum negentropy production (PMNEP) for dynamic order evolution. These principles are the counterparts of the existing entropy principle and the law of maximum entropy production, respectively. The PMNEP encompasses the basic concepts in the evolution postulates by Darwin and de Vries. Perspectives of dynamic order evolution in literature point to the validity of PMNEP as the law of evolution. These two additional principles now enable unified explanation of order creation, existence, evolution, and destruction; using thermodynamics.

We perform single-molecule spatial tracking measurements of a DNA repair protein, the C-terminal domain of Ada (C-Ada) from Escherichia coli, moving on DNA extended by flow. The trajectories of single proteins labeled with a fluorophore are constructed. We analyze single-protein dwell times on DNA for different flow rates and conclude that sliding (with essentially no hopping) is the mechanism of C-Ada motion along stretched DNA. We also analyze the trajectory results with a drift-diffusion Langevin equation approach to elucidate the influence of flow on the protein motion; systematic variation of the flow enables one to estimate the microscopic friction. We integrate the step-size probability distribution to obtain a version of the fluctuation theorem that articulates the relation between the entropy production and consumption under the adjustable drag (i.e., bias) from the flow. This expression allows validation of the Langevin equation description of the motion. Comparison of the rate of sliding with recent computer simulations of DNA repair suggests that C-Ada could conduct its repair function while moving at near the one-dimensional diffusion limit.

The fluctuation theorem gives a mathematical expression to quantify the probability of observing events violating the second law of thermodynamics in a small system over a short period of time. The theorem predicts the ratio of forward (entropy-producing) runs to the backward (entropy-consuming) runs for a nanometer-sized molecular machine in a nonequilibrium system. However, few experimental verifications of the theorem have been carried out. In this paper, I show that the Ussing flux ratio, the ratio of outward to inward unidirectional ion fluxes across a membrane channel, can be derived from the fluctuation theorem if we consider the ion channel and the contacting solutions as a small nonequilibrium system. The entropy change due to ion electrodiffusion is expressed from the fundamental equation for the entropy change. Thus, the empirical flux ratio equation can be interpreted from the more general fluctuation theorem, and serves as a verification of the theorem.

Nanotechnologies take now a wide interest both in the applied and fundamental concerns. The interfacial properties of nano-particles at the fluid–fluid interfaces question the physicist on the extension of the Gibbs surface thermodynamics to interfaces in which nano-particles are entrapped as dispersion stabilizers [K.D. Danov, P.A. Kralchevsky, J. Colloid Interface Sci. 298 (2006) 213] (foams or emulsions). An attempt is proposed to give the physical meaning of the measured surface properties of nano-particles attached to fluid–fluid interfaces like the so-called dynamic surface tension and surface dilational elasticity of suspensions in terms of wetting of the particles at the interface. The Hill [T.L. Hill, Thermodynamics of Small Systems, W.A. Benjamin, New York, 1963] theory for small systems linked to the dissipation fluctuation theorem should give a deeper insight in the statistical mechanics understanding of the interfacial region in which nano-particles are imbedded.

We show that there exists a natural way to define a condition of generalized thermal equilibrium between systems governed by Tsallis thermostatistics, under the hypotheses that i) the coupling between the systems is weak, ii) the structure functions of the systems have a power-law dependence on the energy. It is found that the q values of two such systems at equilibrium must satisfy a relationship involving the respective numbers of degrees of freedom. The physical properties of a Tsallis distribution can be conveniently characterized by a new parameter eta which can vary between 0 and + infinite, these limits corresponding respectively to the two opposite situations of a microcanonical distribution and of a distribution with a predominant power-tail at high energies. We prove that the statistical expression of the thermodynamic functions is univocally determined by the requirements that a) systems at thermal equilibrium have the same temperature, b) the definitions of temperature and entropy are consistent with the second law of thermodynamics. We find that, for systems satisfying the hypotheses i) and ii) specified above, the thermodynamic entropy is given by Renyi entropy., Comment: 14 pages, 1 figure, revised version accepted for publication in Physica A

Recent results on the stationary state Fluctuation Theorems for work and heat fluctuations of Langevin systems are presented. The relevance of finite time corrections in understanding experimental and simulation results is explained in the context of an exactly solvable model, namely a Brownian particle in a harmonic potential, which is dragged through the surrounding fluid. In this model, work fluctuations obey the conventional form of the fluctuation theorem while heat fluctuations satisfy an extended form. The connection with other work in recent literature is pointed out, and further generalizations are suggested., 12 pages, 2 figures. Contribution to Proceedings of "Work, Dissipation, and Fluctuations in Nonequilibrium Physics", Brussels, 2006

We analyse the different situations where a fluctuation theorem can be proved for a single macroscopic current of a system in a nonequilibrium steady state sustaining several transport processes. We express the conditions under which such a fluctuation theorem will hold in terms of the cycles and transport processes of the network. In this case, a given macroscopic current obeys a fluctuation theorem regardless of the other transport processes. To cite this article: D. Andrieux, P. Gaspard, C. R. Physique 8 (2007).

Fluctuation Theorems are statements about the entropy of systems far from thermal equilibrium. In this Letter relativistic Fluctuation Theorems for Brownian motion are presented and proven. Though there is a known discretization dilemma leading to a certain class of Brownian processes, the Fluctuation Theorems are shown to cover the entire class, and to determine the physical process within this class. In the general-relativistic case the heat responsible for entropy production is the exchanged 4-momentum projected on the local time axis of the heat bath., 4 pages, 1 figure

Hasselt Univ, B-3590 Diepenbeek, Belgium. Univ Alabama, Dept Phys, Birmingham, AL 35294 USA.CLEUREN, B, Hasselt Univ, Agoralaan Ggebouw D, B-3590 Diepenbeek, Belgium.bart.cleuren@uhasselt.be christian.vandenbroeck@uhasselt.be kawai@uab.edu

Quantum extensions of the Gallavotti-Cohen fluctuation theorem (FT) for the entropy production have been discussed by several authors. There is a practical gap between microscopic forms of FT and mesoscopic (i.e. not purely Hamiltonian) forms for open systems. In a microscopic setup, it is easy to state and to prove FT. In a mesoscopic setup, it is difficult to identify fluctuations of the entropy production. (This difficulty is absent in the classical case.) We discuss a particular mesoscopic model: a Lindblad master equation, in which we state FT and, more importantly, connect it rigorously with the underlying microscopic FT. We also remark that FT is satisfied by the Lesovik-Levitov formula for statistics of charge transport., Comment: Conference Proceedings (Brussels, march 2006), 10 pages, to appear in Comptes rendus - Physique

An elegant but seldom appreciated effort to provide a mechanical model of equilibrium thermodynamics dates back to the Helmholtz theorem (HT). According to this theorem, the thermodynamic relations hold mechanically (without probabilistic assumptions) in the case of one-dimensional monocyclic systems. Thanks to a discrete picture of the phase space, Boltzmann was able to apply the HT to multi-dimensional ergodic systems, suggesting that the thermodynamic relations we observe in macroscopic systems at equilibrium are a direct consequence of the microscopic laws of dynamics alone. Here I review Boltzmann’s argument and show that, using the language of the modern ergodic theory, it can be safely re-expressed on a continuumphase space as a generalized Helmholtz theorem(GHT), which can be readily proved. Along the way the agreement between the Helmholtz–Boltzmann theory and that of P. Hertz (based on adiabatic invariance) is revealed. Both theories, in fact, lead to define the entropy as the logarithmof the phase-space volum e enclosed by the constant energy hypersurface (volume entropy). r 2005 Elsevier Ltd. All rights reserved.

The Fluctuation Theorem (FT) is a generalisation of the Second Law of Thermodynamics that applies to small systems observed for short times. For thermostatted systems it gives the probability ratio that entropy will be consumed rather than produced. In this paper we derive the Transient and Steady State Fluctuation Theorems using Lyapunov weights rather than the usual Gibbs weights. At long times the Fluctuation Theorems so derived are identical to those derived using the more standard Gibbs weights., Comment: 26 pages; to appear in Physica D

On the basis of complete distribution normalization Tr ρ =1 and unnormalized average energy E= Tr ρ q H , we show an attempt to establish the zeroth law of thermodynamics within the framework of nonextensive statistical mechanics for canonical ensemble. The first law of thermodynamics and the statistical interpretation of heat and work are discussed.

This paper investigates what the source of time-asymmetry is in thermodynamics, and comments on the question whether a time-symmetric formulation of the Second Law is possible.

The aim of this article is to analyze the relation between the second law of thermodynamics and the so-called arrow of time. For this purpose, a number of different aspects in this arrow of time are distinguished, in particular those of time-(a)symmetry and of (ir)reversibility. Next I review versions of the second law in the work of Carnot, Clausius, Kelvin, Planck, Gibbs, Carath\'eodory and Lieb and Yngvason, and investigate their connection with these aspects of the arrow of time. It is shown that this connection varies a great deal along with these formulations of the second law. According to the famous formulation by Planck, the second law expresses the irreversibility of natural processes. But in many other formulations irreversibility or even time-asymmetry plays no role. I therefore argue for the view that the second law has nothing to do with the arrow of time. Key words: thermodynamics, second law, irreversibility, time-asymmetry, arrow of time., Comment: Studies in History and Philosophy of Modern Physics (to appear)

Gibbs’ theorem valid for systems with the extensive entropy is generalized for systems possessing nonextensive entropies, and macroscopic thermodynamics of equilibrium is established for systems obeying the power-law distributions.

Fluctuation of mean Lyapunov exponent for the coupled map lattice of logistic map is studied. Theorem by Gallavotti and Cohen for many particle systems is applied to the coupled map lattice model. It is shown that the fluctuation of mean Lyapunov exponent for the model satisfies the extended form of the fluctuation theorem by them. The concept of the mean Lyapunov exponent introduced in this paper turns out to be realistic as well as the one for many particle systems. As a result, the relation between mean Lyapunov exponent and entropy production rate is derived.

A flux fluctuation theorem proposed recently [Seitaridou, et al., J. Phys. Chem. B 111 (2007) 2288] on the relative probability of direct and reverse diffusion fluxes in a non-equilibrium steady state is related here to a non-equilibrium thermodynamic potential used in extended irreversible thermodynamics. This connection allows one to provide a new derivation of the theorem, which complements the previous one, to generalize it to other fluxes, and illustrates the thermodynamic relevance of this theorem.

The fluctuation-dissipation theorem is generalized to the case of nonequilibrium (albeit in a stable steady state) systems. The relationship between the correlation function of the current fluctuations and the average energy absorbed by the system as a consequence of dissipation is used. For a nonequilibrium classical system, the responce function is connected with the correlation function in which the averaging is over the derivative of the energy distribution function. Using the spectrum of the electromagnetic fluctuations, inverting the fluctuation-dissipation relation one can find the permittivity of the medium.

A mechanism for the validity of a local version of the fluctuation theorem, uniform in the system size, is discussed for a reversible chain of weakly coupled Anosov systems., plain TeX, 1 figure

A closed macroscopic system with fluctuating local properties is treated as a thermodynamic system with internal degrees of freedom. Gibb’s entropy postulate is used to define the systems’ entropy as a functional of the probability density in internal coordinate space. It is shown that application of the scheme of thermodynamics of irreversible processes then leads directly to the theory of fluctuations as Markov processes described by a multivariate Fokker–Planck equation. In this perspective fluctuation theory may be said to have become integrated into non-equilibrium thermodynamics.

Given a nonequilibrium steady state ϱ we derive formally the linear response formula for the variation of an expectation value at time t under a time-dependent infinitesimal perturbation δτF of the acting forces. This leads to a form of the fluctuation-dissipation theorem valid far from equilibrium: the complex singularities of the susceptibility are in part those of the spectral density, and in part of a different nature to be discussed.

Recently we have put forward the efficacy of single residue perturbations for a protein to populate its alternative conformational states[1-3]. In this work, we explain why mutation or protonation of a single-residue can create substantial conformational changes. First, we introduce a methodology which couples the network-based perturbation-response scanning (PRS) technique[4] with repeated constant force-steered molecular dynamics (CF-SMD)[5] simulations. Second, we utilize Crooks’ fluctuation theorem[6] to measure the free-energy differences between conformational states to classify the circumstances under which a mutation or protonation achieves population shifts. Finally, we trace the relationship between the non-equilibrium trajectories(NET) from CF-SMD and redundant pathways in residue networks[1], and employ this relationship in interpreting the outcomes of the fluctuation theorems so as to ferret out the degree of collectivity in residue fluctuations.Here are the procedure and sample results for calmodulin: (i)PRS takes the most-populated calmodulin conformation(3cln) and identifies E31whose directional-sensitive perturbations results in positional changes that yields the best overlap with considerably less populated states[7,2];(ii) through extensive MD simulations, E31A mutation reproduces structures consistent with those from NMR experiments[8];(iii) repeated CF-SMD runs for E31A produce NET between the two states, while those for E31 protonation do not;(iv) via Crooks’ fluctuation theorem, we find the free-energy barrier between the two states to be +0.60kcal/mole for E31A. E31A MD runs reproduce conformational changes between states three orders of magnitude faster than in wild type[7]. Analysis of the NET for redundant paths reveals collectivity induced by strategically inserted point mutations.1. Atilgan et al., Annu. Rev. Biophys. 41, 205(2012).2. Atilgan et al., J. Chem. Phys. 135, 155102(2011).3. Atilgan et al., Biophys. J. 99, 933(2010).4. Atilgan and Atilgan, PLoS Comput. Biol. 5, e1000544(2009).5. Izrailev et al., Biophys. J.72, 1568(1997).6. Crooks, Phys.Rev.E 60, 2721(1999).7. Slaughter et al., J.Phys.Chem.B 109, 12658(2005).8. Gsponer et al., Structure 16, 736(2008).

On the basis of the equation of motion for a RLC circuit with source, the energy fluctuation of the circuit is discussed by using the fluctuation-dissipation theorem. It is found that the fluctuation is a quantum effect at low temperature but becomes a classical thermodynamic effect when the temperature increases. We have quantized the circuit at zero temperature, and obtained the fluctuations of charge and current as well as the uncertainty relation.

In a finite population game, the strategy space should fall into a strategy lattice. In a stochastic evolutionary trajectory (Fig. 1), many cycles (generalized Shapley loop) could be filtered out (Table 1). The cycles associated with the stochastic process describe the time evolution. Referring to the direction of the path and the unit size of the lattice (Fig. 1), the amplitude of a cycle must be an integer. The cycles and their amplitudes and then the probability spectrum of the amplitude can be obtained.Data comes from Standard RPS population games. Subjects are random matching paired each round. 300 rounds are repeated in each of the 12 sessions in each treatment whose population size is 4, 6 and 8 respectively. In these games, Nash random and independent inference is the spectrum should be symmetry but Shapley inference is asymmetry.Results are (1) We provide, firstly, the spectrum of cycle amplitude (Fig. 2) from RPS population game; (2) Observed the spectrum is asymmetry (unbalance in /- amplitude and Tab. 2) rejects Nash prediction and supports Shapley prediction significant; (3) Interesting is that the characters of the observed spectrum consists with - the extended second law of thermodynamics - fluctuation theorems.In Summary, in the trajectories, even thought the cycles are erratic, but the distribution of the cycles amplitudes has its own regularity. With this finding, also supported from the observations in the experiments, we suggest that the so called erratic processes of the laboratory social evolution is intrinsic and obey fluctuation theorems.

In game, with the individual interactions, the social state is changing stochastically and governed by Nash Equilibrium in the strategy space. With the method from the physics of nonequlibrium steady state (NESS) and the data from experimental economics treatments (EET), we obtain the social transition spectrums and from which, the kink phenomena and the fluctuation theorem predictions in NESS are supported. The data comes from the fi xed paired 2-person constant sum 2x2 games with unique mixed strategy Nash equilibrium (MSNE). These findings demonstrate the new experimetric for social dynamics, meanwhile, an indiff erence within social and physical systems.

This article establishes for a class of evolutionary processes, a directionality theorem which is an analogue of the second law of thermodynamics. For populations evolving under limited resource conditions the effect of mutation and selection will result in the spontaneous transition from one stationary state to another. We show that this transition is described by an increase in population entropy, a parameter which measures the diversity of lineages induced by the birth and death rates of the individuals in the population. The second law of thermodynamics refers to systems in an adiabatic enclosure and describe an increase in geometric complexity as the system moves from one equilibrium steady state to another. The directionality theorem in evolutionary dynamics refers to populations subject to limited resource conditions and describes an increase in dynamic complexity as the system moves from one nonequilibrium steady state to another. We invoke a formal correspondence between the evolutionary parameter, generation time and the thermodynamic parameter, temperature, established in J. Stat. Phys. 30 (1983) 709, to show that in populations evolving under the additional constraint of constant generation time, the increase in population entropy reduces to an increase in geometric complexity, a property which is formally identical to the second law.

The dissociation of inter- and intra-molecular bonds by force is a process that occurs regularly in biological machinery and many cellular events. Forcing such transitions in a controlled environment has also emerged as a modern practice in the laboratory for studies of the physical principles of bond lifetimes and protein unfolding. It is commonly assumed that force-driven dissociation is irreversible, which leads to the analysis of first-passage statistics and results in simple analytical results for the distribution and moments of the transition force. However, the irreversible model is a first-order approximation which is only valid very far from equilibrium, or under specific irreversible circumstances. Furthermore, the irreversible model has led many to conclude that force spectra that deviate from linearity unequivocally represent multiple energy barriers along the intermolecular reaction coordinate.We show that irreversible first-passage analysis, which fails for two-state systems, can be replaced by analyzing the conditional single-passage time between the two states. We find simple solutions for the forward and time-reversed distributions of the transition force, and the isothermal work, which analytically satisfy the fluctuation theorem. We also define how stochastic force trajectories should be measured when multiple forward-reverse events occur. By accounting for reversibility, we show that both the distribution and the first moment of the rupture force significantly differ from the irreversible model and clearly connect with the equilibrium regime. We find that the resulting spectrum of rupture forces is not monotonic with log of the loading rate, but follows at least two major regimes - a linear-response and a dynamic response - with the linear regime tending to the equilibrium free energy change. We validate our analytical results with simulations and experimental data on bond rupture and protein unfolding.

On the basis of a complete system of fluctuation-dissipation relations, considered in the first part of this series, a variational principle for nonlinear irreversible processes is derived. According to this principle the virtual entropy production functional (analogous to the action in mechanics) has an absolute minimum meaning on the real trajectory of a system. The universal structure of the “kinetic potential” and the “lagrangian” of a system, each contain complete information about fluctuations of macrovariables. The connection of the lagrangian with the markovian kinetic operator of macrovariables is stated. Fundamental properties of dissipative potentials, reflecting microscopic reversibility, are considered. The derived variational principle can be applied to closed systems (the steady state of which is equilibrium) as well as to open ones (when external dynamic forces cause entropy flux through the system and put it into a steady non-equilibrium state). Canonical transformations of macrovariables are considered.