On the fast and the slow components of thermal fluctuations (original) (raw)
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Hydrodynamical fluctuations in extended irreversible thermodynamics
Starting from the generalized Gibbs equation of extended irreversible thermodynamics, we define a thermodynamic potential that provides a suitable description of the fluctuations of the hydrodynamical dissipative fluxes when it is used in an expression analogous to the classical Einstein formula for the probability of fluctuations. In the limit of vanishing relaxation times, our results coincide with those of Landau-Lifshitz. The effect of the rapid normal modes is taken into account as a stochastic noise in the evolution equations of the dissipative fluxes, and their covariance matrix is found from a fluctuation-dissipation theorem.
Journal of Statistical Physics, 1982
The Ventsel'-Freidlin probability estimates for small random perturbations of dynamical systems are used to generalize and justify the Onsager-Machlup irreversible thermodynamic variational description of Gaussian statistical distributions in the limit where Boltzmann's constant tends to zero for non-Gaussian diffusion processes. A Hamiltonian formulation is used to determine the maximum likelihood paths for the growth and decay of nonequilibrium fluctuations, in the same limit, subject to the imposed constraints. The paths of maximum likelihood manifest a symmetry in past and future and are the stationary conditions of the constrained thermodynamic variational principle of least dissipation of energy. The power balance equations supply the required constraints and the most likely path for the growth of a fluctuation is characterized by a negative entropy production. The entropy plays the role of the quasipotential of Ventsel' and Freidlin and exit from a bounded domain containing a deterministically stable steady state is made at that state on the boundary with maximum entropy.
Thermodynamic time asymmetry in non-equilibrium fluctuations
Journal of Statistical Mechanics-theory and Experiment, 2008
We here present the complete analysis of experiments on driven Brownian motion and electric noise in a RC circuit, showing that thermodynamic entropy production can be related to the breaking of time-reversal symmetry in the statistical description of these nonequilibrium systems. The symmetry breaking can be expressed in terms of dynamical entropies per unit time, one for the forward process and the other for the time-reversed process. These entropies per unit time characterize dynamical randomness, i.e., temporal disorder, in time series of the nonequilibrium fluctuations. Their difference gives the well-known thermodynamic entropy production, which thus finds its origin in the time asymmetry of dynamical randomness, alias temporal disorder, in systems driven out of equilibrium. PACS numbers: 05.70.Ln; 05.40.-a; 02.50.Ey
On the foundations of extended irreversible thermodynamics
Journal of Statistical Physics, 1984
A theory of macroscopic systems which takes as independent variables the slow (conserved) ones plus the fast dissipative fluxes is carefully analyzed at three levels of description: macroscopic (thermodynamic), microscopic (projection operators) and mesoscopic (fluctuation theory). Such a description is compared with the memory function approach based only on the conserved variables. We find that the first theory is richer and wider than the second one, and some misunderstandings in this connection are clarified and discussed.
Time Reversibility, Correlation Decay and the Steady State Fluctuation Relation for Dissipation
Entropy, 2013
Steady state fluctuation relations for nonequilibrium systems are under intense investigation because of their important practical implications in nanotechnology and biology. However the precise conditions under which they hold need clarification. Using the dissipation function, which is related to the entropy production of linear irreversible thermodynamics, we show time reversibility, ergodic consistency and a recently introduced form of correlation decay, called T-mixing, are sufficient conditions for steady state fluctuation relations to hold. Our results are not restricted to a particular model and show that the steady state fluctuation relation for the dissipation function holds near or far from equilibrium subject to these conditions. The dissipation function thus plays a comparable role in nonequilibrium systems to thermodynamic potentials in equilibrium systems.
Fluctuation symmetries for work and heat
Physical Review E, 2006
We consider a particle dragged through a medium at constant temperature as described by a Langevin equation with a time-dependent potential. The time-dependence is specified by an external protocol. We give conditions on potential and protocol under which the dissipative work satisfies an exact symmetry in its fluctuations for all times. We also present counter examples to that exact fluctuation symmetry when our conditions are not satisfied. Finally, we consider the dissipated heat which differs from the work by a temporal boundary term. We explain why there is a correction to the standard fluctuation theorem due to the unboundedness of that temporal boundary. However, the corrected fluctuation symmetry has again a general validity.
Thermodynamic constraints on fluctuation phenomena
The relationships among reversible Carnot cycles, the absence of perpetual motion machines, and the existence of a nondecreasing globally unique entropy function form the starting point of many textbook presentations of the foundations of thermodynamics. However, the thermal fluctuation phenomena associated with statistical mechanics has been argued to restrict the domain of validity of this basis of the second law of thermodynamics. Here we demonstrate that fluctuation phenomena can be incorporated into the traditional presentation, extending rather than restricting the domain of validity of the phenomenologically motivated second law. Consistency conditions lead to constraints upon the possible spectrum of thermal fluctuations. In a special case this uniquely selects the Gibbs canonical distribution and more generally incorporates the Tsallis distributions. No particular model of microscopic dynamics need be assumed.
N ov 2 00 7 Thermodynamic time asymmetry in nonequilibrium fluctuations
2021
We here present the complete analysis of experiments on driven Brownian motion and electric noise in a RC circuit, showing that thermodynamic entropy production can be related to the breaking of time-reversal symmetry in the statistical description of these nonequilibrium systems. The symmetry breaking can be expressed in terms of dynamical entropies per unit time, one for the forward process and the other for the time-reversed process. These entropies per unit time characterize dynamical randomness, i.e., temporal disorder, in time series of the nonequilibrium fluctuations. Their difference gives the well-known thermodynamic entropy production, which thus finds its origin in the time asymmetry of dynamical randomness, alias temporal disorder, in systems driven out of equilibrium.
Fluctuations in Stationary Nonequilibrium States of Irreversible Processes
Physical Review Letters, 2001
In this paper we formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which covers situations in a nonlinear hydrodynamic regime and is verified explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Our results include the modification of the Onsager-Machlup theory in the SNS, a general Hamilton-Jacobi equation for the macroscopic entropy and a non equilibrium, non linear fluctuation dissipation relation valid for a wide class of systems. PACS numbers: 05.20.-y, 05.40.-a, 05.60.-k