A nonequilibrium temperature and fluctuation theorem for soft-mode turbulence

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.     

Entropy production along a stochastic trajectory and an integral fluctuation theorem

For stochastic nonequilibrium dynamics like a Langevin equation for a colloidal particle or a master equation for discrete states, entropy production along a single trajectory is studied. It involves both genuine particle entropy and entropy production in the surrounding medium. The integrated sum of both Delatas(tot) is shown to obey a fluctuation theorem (exp([-Deltas(tot) = 1 for arbitrary initial conditions and arbitrary time-dependent driving over a finite time interval.     

Entropy production and time asymmetry in nonequilibrium fluctuations

The time-reversal symmetry of nonequilibrium fluctuations is experimentally investigated in two out-of-equilibrium systems: namely, a Brownian particle in a trap moving at constant speed and an electric circuit with an imposed mean current. The dynamical randomness of their nonequilibrium fluctuations is characterized in terms of the standard and time-reversed entropies per unit time of dynamical systems theory. We present experimental results showing that their difference equals the thermodynamic entropy production in units of Boltzmann's constant.     

Near-equilibrium measurements of nonequilibrium free energy

A central endeavor of thermodynamics is the measurement of free energy changes. Regrettably, although we can measure the free energy of a system in thermodynamic equilibrium, typically all we can say about the free energy of a nonequilibrium ensemble is that it is larger than that of the same system at equilibrium. Herein, we derive a formally exact expression for the probability distribution of a driven system, which involves path ensemble averages of the work over trajectories of the time-reversed system. From this we find a simple near-equilibrium approximation for the free energy in terms of an excess mean time-reversed work, which can be experimentally measured on real systems. With analysis and computer simulation, we demonstrate the accuracy of our approximations for several simple models.     

非平衡功与自由能差的关系

以一个受迫谐振子为对象证明了Jarzynski等式,即两平衡态的自由能差可以用它们之间非平衡功的指数平均来表示,这里两个态的转换是在有限时间完成的.当外部驱动力是一个周期信号时,发现外界对系统所做的广义功存在一个共振现象.     

Entropy production in nonequilibrium systems at stationary states

We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is performed by placing the system in contact with two reservoirs with distinct sets of thermodynamic fields and by assuming an appropriate form for the transition rate. The approach is applied to an interacting lattice gas model in contact with two heat and particle reservoirs. On a square lattice, a continuous symmetry breaking phase transition takes place such that at the nonequilibrium ordered phase a heat flow sets in even when the temperatures of the reservoirs are the same. The entropy production rate is found to have a singularity at the critical point of the linear-logarithm type.     

Quantum work fluctuation theorem: Nonergodic Brownian motion case

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.     

The vacuum fluctuation theorem: Exact Schrödinger equation via nonequilibrium thermodynamics

Assuming that a particle of energy ?ω is actually a dissipative system maintained in a nonequilibrium steady state by a constant throughput of energy (heat flow), one obtains the shortest derivation of the Schrödinger equation from (modern) classical physics in the literature, and the only exact one, too.     

Hydrodynamics and the fluctuation theorem

The fluctuation theorem is a pivotal result of statistical physics. It quantifies the probability of observing fluctuations which are in violation of the second law of thermodynamics. More specifically, it quantifies the ratio of the probabilities of observing entropy-producing and entropy-consuming fluctuations measured over a finite volume and time span in terms of the rate of entropy production in the system, the measurement volume, and time. We study the fluctuation theorem in computer simulations of planar shear flow. The simulations are performed by employing the method of multiparticle collision dynamics, which captures both thermal fluctuations and hydrodynamic interactions. The main outcome of our analysis is that the fluctuation theorem is verified at any averaging time provided that the measurement volume exhibits a specific dependence on a hydrodynamic time scale.     

Total entropy production fluctuation theorems in a nonequilibrium time-periodic steady state

We investigate the total entropy production of a Brownian particle in a driven bistable system. This system exhibits the phenomenon of stochastic resonance. We show that in the time-periodic steady state, the probability density function for the total entropy production satisfies Seifert’s integral and detailed fluctuation theorems over finite time trajectories.     

Optimal estimates of free energies from multistate nonequilibrium work data

We derive the optimal estimates of the free energies of an arbitrary number of thermodynamic states from nonequilibrium work measurements; the work data are collected from forward and reverse switching processes and obey a fluctuation theorem. The maximum likelihood formulation properly reweights all pathways contributing to a free energy difference and is directly applicable to simulations and experiments. We demonstrate dramatic gains in efficiency by combining the analysis with parallel tempering simulations for alchemical mutations of model amino acids.     

Exact free energy functional for a driven diffusive open stationary nonequilibrium system

We obtain the exact probability exp[-LF([rho(x)])] of finding a macroscopic density profile rho(x) in the stationary nonequilibrium state of an open driven diffusive system, when the size of the system L-->infinity. F, which plays the role of a nonequilibrium free energy, has a very different structure from that found in the purely diffusive case. As there, F is nonlocal, but the shocks and dynamic phase transitions of the driven system are reflected in nonconvexity of F, in discontinuities in its second derivatives, and in non-Gaussian fluctuations in the steady state.     

Kinesin and the Crooks fluctuation theorem

The thermal efficiency of the kinesin cycle at stalling is presently a matter of some debate, with published predictions ranging from 0 [Phys. Rev. Lett. 99, 158102 (2007); Phys. Rev. E 78, 011915 (2008)] to 100% [in Molecular Motors, edited by M. Schliwa (Wiley-VCH Verlag GmbH, Weinheim (2003), p. 207]. In this note we attemp to clarify the issues involved. We also find an upper bound on the kinesin efficiency by constructing an ideal kinesin cycle to which the real cycle may be compared. The ideal cycle has a thermal efficiency of less than one, and the real one is less efficient than the ideal one always, in compliance with Carnot’s theorem.     

Entropy,the central limit theorem and the algebra of the canonical commutation relation

The central limit theorem of Cushen and Hudson is reformulated on the algebra of the CCR. Namely, for a gauge invariant state , the weighted convolutions _n of the central limit tend to the quasi-free reduction _Q of pointwise. It is proved that if the initial relative entropy S(, _Q ) is finite, then S( _n , _Q ) goes to 0 and so _n – _Q 0. No restriction on the dimension of the test function space is made.     

Extension of the fluctuation theorem

Heat fluctuations are studied in a dissipative system with both deterministic and stochastic components for a simple model: a Brownian particle dragged through water by a moving potential. An extension of the stationary state fluctuation theorem is derived. For infinite time, this reduces to the conventional fluctuation theorem only for small fluctuations; for large fluctuations, it gives a much larger ratio of the probabilities of the particle to absorb rather than supply heat. This persists for finite times and should be observable in experiments similar to a recent one carried out by Wang et al.     

Entropy production and thermodynamics of nonequilibrium stationary states: a point of view

Entropy might be a not well defined concept if the system can undergo transformations involving stationary nonequilibria. It might be analogous to the heat content (once called "caloric") in transformations that are not isochoric (i.e., which involve mechanical work): it could be just a quantity that can be transferred or created, like heat in equilibrium. The text first reviews the philosophy behind a recently proposed definition of entropy production in nonequilibrium stationary systems. A detailed technical attempt at defining the entropy of a stationary states via their variational properties follows: the unsatisfactory aspects of the results add arguments in favor of the nonexistence of a function of state to be identified with entropy; at the same time new aspects and properties of the phase space contraction emerge.     

Levy stability for anisotropic dynamical fluctuation in high energy multiparticle production

The behaviour of Levy indexμ in various phase space dimensions is studied. The reason for the violation of Levy stable condition at three-dimension observed in experiment is investigated. It is shown that the apparent violation of Levy stable condition may be due to the wrong isotropic analysis for the highly anisotropic phase space of multiparticle production.     

Levy stability for anisotropic dynamical fluctuation in high energy multiparticle production

The behaviour of Levy index 7 in various phase space dimensions is studied. The reason for the violation of Levy stable condition at three-dimension observed in experiment is investigated. It is shown that the apparent violation of Levy stable condition may be due to the wrong isotropic analysis for the highly anisotropic phase space of multiparticle production.