Entropy production and time asymmetry in nonequilibrium fluctuations

Lower bounds on dissipation upon coarse graining

By different coarse-graining procedures, we derive lower bounds on the total mean work dissipated in Brownian systems driven out of equilibrium. With several analytically solvable examples, we illustrate how, when, and where the information on the dissipation is captured.

Continuous-time random walk for open systems: fluctuation theorems and counting statistics

We consider continuous-time random walks (CTRW) for open systems that exchange energy and matter with multiple reservoirs. Each waiting time distribution (WTD) for times between steps is characterized by a positive parameter alpha , which is set to alpha=1 if it decays at least as fast as t{-2} at long times and therefore has a finite first moment. A WTD with alpha<1 decays as t{-alpha-1} . A fluctuation theorem for the trajectory quantity R , defined as the logarithm of the ratio of the probability of a trajectory and the probability of the time reversed trajectory, holds for any CTRW. However, R can be identified as a trajectory entropy change only if the WTDs have alpha=1 and satisfy separability (also called "direction time independence"). For nonseparable WTDs with alpha=1 , R can only be identified as a trajectory entropy change at long times, and a fluctuation theorem for the entropy change then only holds at long times. For WTDs with 0<alpha<1 no meaningful fluctuation theorem can be derived. We also show that the (experimentally accessible) nth moments of the energy and matter transfers between the system and a given reservoir grow as t{nalpha} at long times.

Temporal disorder and fluctuation theorem in chemical reactions

We report the analytical study of a class of chemical reactions described as birth-and-death stochastic processes ruled by a master equation compatible with the mass action law of chemical kinetics. We solve analytically this master equation to find the generating functions of the fluctuating fluxes and of the Lebowitz-Spohn action functional. These generating functions are explicitly shown to obey fluctuation theorems. In the case of fluxes, we derive relations for the nonlinear response coefficients, extending Onsager's reciprocity relations. Moreover, symmetry relations reminiscent of the fluctuation theorem are obtained for the finite-time probability distributions of the fluxes. The temporal disorder of the stochastic process is also characterized and related to the thermodynamic entropy production.

Mapping nonequilibrium onto equilibrium: the macroscopic fluctuations of simple transport models

We study a simple transport model driven out of equilibrium by reservoirs at the boundaries, corresponding to the hydrodynamic limit of the symmetric simple exclusion process. We show that a nonlocal transformation of densities and currents maps the large deviations of the model into those of an open, isolated chain satisfying detailed balance, where rare fluctuations are the time reversals of relaxations. We argue that the existence of such a mapping is the immediate reason why it is possible for this model to obtain an explicit solution for the large-deviation function of densities through elementary changes of variables. This approach can be generalized to the other models previously treated with the macroscopic fluctuation theory.