Fluctuation relations for diffusion that is thermally driven by a nonstationary bath

Finite-Time Dynamical Phase Transition in Nonequilibrium Relaxation

We uncover a finite-time dynamical phase transition in the thermal relaxation of a mean-field magnetic model. The phase transition manifests itself as a cusp singularity in the probability distribution of the magnetization that forms at a critical time. The transition is due to a sudden switch in the dynamics, characterized by a dynamical order parameter. We derive a dynamical Landau theory for the transition that applies to a range of systems with scalar, parity-invariant order parameters. Close to criticalilty, our theory reveals an exact mapping between the dynamical and equilibrium phase transitions of the magnetic model, and implies critical exponents of mean-field type. We argue that interactions between nearby saddle points, neglected at the mean-field level, may lead to critical, spatiotemporal fluctuations of the order parameter, and thus give rise to novel, dynamical critical phenomena.

Nonequilibrium nature of adaptation in bacterial chemotaxis: A fluctuation-dissipation theorem approach

Adaptation is a crucial biological function possessed by many sensory systems. In this paper, we show that the fluctuation-dissipation theorem (FDT) serves as an ideal mathematical tool to study adaptation. With the aid of the nonequilibrium FDT developed by Seifert and Speck [Europhys. Lett. 89, 10007 (2010)EULEEJ0295-507510.1209/0295-5075/89/10007], we demonstrate the nonequilibrium nature of adaptation in bacterial chemotaxis. We further show that nonequilibrium is a necessary condition for adaptation even beyond the linear response regime using the spectral theory of generator matrices. In particular, the results of this paper are irrelevant to the specific functional forms of the model parameters. This suggests that the nonequilibrium nature of adaptation is a topological property, rather than a geometric property, of the underlying biochemical reaction network.

Thermal response of nonequilibrium RC circuits

We analyze experimental data obtained from an electrical circuit having components at different temperatures, showing how to predict its response to temperature variations. This illustrates in detail how to utilize a recent linear response theory for nonequilibrium overdamped stochastic systems. To validate these results, we introduce a reweighting procedure that mimics the actual realization of the perturbation and allows extracting the susceptibility of the system from steady-state data. This procedure is closely related to other fluctuation-response relations based on the knowledge of the steady-state probability distribution. As an example, we show that the nonequilibrium heat capacity in general does not correspond to the correlation between the energy of the system and the heat flowing into it. Rather, also nondissipative aspects are relevant in the nonequilibrium fluctuation-response relations.

Fluctuation theorems and inequalities generalizing the second law of thermodynamics out of equilibrium

We present a general framework for systems which are prepared in a nonstationary nonequilibrium state in the absence of any perturbation and which are then further driven through the application of a time-dependent perturbation. By assumption, the evolution of the system must be described by Markovian dynamics. We distinguish two different situations depending on the way the nonequilibrium state is prepared; either it is created by some driving or it results from a relaxation following some initial nonstationary conditions. Our approach is based on a recent generalization of the Hatano-Sasa relation for nonstationary probability distributions. We also investigate whether a form of the second law holds for separate parts of the entropy production and for any nonstationary reference process, a question motivated by the work of M. Esposito et al. [Phys. Rev. Lett. 104, 090601 (2010)]. We find that although the special structure of the theorems derived in this reference is not recovered in the general case, detailed fluctuation theorems still hold separately for parts of the entropy production. These detailed fluctuation theorems contain interesting generalizations of the second law of thermodynamics for nonequilibrium systems.

Inequalities generalizing the second law of thermodynamics for transitions between nonstationary states

We discuss the consequences of a variant of the Hatano-Sasa relation in which a nonstationary distribution is used in place of the usual stationary one. We first show that this nonstationary distribution is related to a difference of traffic between the direct and dual dynamics. With this formalism, we extend the definition of the adiabatic and nonadiabatic entropies introduced by M. Esposito and C. Van den Broeck in Phys. Rev. Lett. 104, 090601 (2010) for the stationary case. We also obtain interesting second-law-like inequalities for transitions between nonstationary states.

Heat fluctuations in a nonequilibrium bath

We measure the energy fluctuations of a Brownian particle confined by an optical trap in an aging gelatin after a very fast quench (less than 1 ms). The strong nonequilibrium fluctuations due to the assemblage of the gel are interpreted, within the framework of fluctuation theorem, as a heat flux from the particle towards the bath. We derive an analytical expression of the heat probability distribution, which fits the experimental data and satisfies a fluctuation relation similar to that of a system in contact with two baths at different temperatures.