Dynamical fluctuations for periodically driven diffusions

We study dynamical fluctuations in overdamped diffusion processes driven by time periodic forces. This is done by studying fluctuation functionals (rate functions from large deviation theory), of fluctuations around the non-equilibrium steady regime. We identify a concept called traffic. This traffic, which was introduced in the context of non-equilibrium steady state statistics, is extended here for time-dependent but periodic forces. We discuss the fluctuation functionals of occupations and currents, and work out some specific examples. The connection between these and non-equilibrium thermodynamic potentials, their corresponding variational principles and their Legendre transforms, are also discussed.Comment: Explicit examples adde

Structures of nonequilibrium fluctuations: dissipation and activity

We discuss research done in two important areas of nonequilibrium statistical mechanics: fluctuation dissipation relations and dynamical fluctuations. In equilibrium systems the fluctuation-dissipation theorem gives a simple relation between the response of observables to a perturation and correlation functions in the unperturbed system. Our contribution here is an investigation of the form of the response function for systems out of equilibrium. Furthermore, we use the theory of large deviations to examine dynamical fluctuations in systems out of equilibrium. In dynamical fluctuation theory we consider two kinds of observables: occupations (describing the fraction of time the system spends in each configuration) and currents (describing the changes of configuration the system makes). We explain how to compute the rate functions of the large deviations, and what the physical quantities are that govern their form.Comment: PhD thesis (defended in may 2010

The modified Sutherland--Einstein relation for diffusive nonequilibria

There remains a useful relation between diffusion and mobility for a Langevin particle in a periodic medium subject to nonconservative forces. The usual fluctuation-dissipation relation easily gets modified and the mobility matrix is no longer proportional to the diffusion matrix, with a correction term depending explicitly on the (nonequilibrium) forces. We discuss this correction by considering various simple examples and we visualize the various dependencies on the applied forcing and on the time by means of simulations. For example, in all cases the diffusion depends on the external forcing more strongly than does the mobility. We also give an explicit decomposition of the symmetrized mobility matrix as the difference between two positive matrices, one involving the diffusion matrix, the other force--force correlations

Entropy and efficiency of a molecular motor model

In this paper we investigate the use of path-integral formalism and the concepts of entropy and traffic in the context of molecular motors. We show that together with time-reversal symmetry breaking arguments one can find bounds on efficiencies of such motors. To clarify this techinque we use it on one specific model to find both the thermodynamic and the Stokes efficiencies, although the arguments themselves are more general and can be used on a wide class of models. We also show that by considering the molecular motor as a ratchet, one can find additional bounds on the thermodynamic efficiency

Fluctuations and response of nonequilibrium states

A generalized fluctuation-response relation is found for thermal systems driven out of equilibrium. Its derivation is independent of many details of the dynamics, which is only required to be first-order. The result gives a correction to the equilibrium fluctuation-dissipation theorem, in terms of the correlation between observable and excess in dynamical activity caused by the perturbation. Previous approaches to this problem are recovered and extended in a unifying scheme

Monotone return to steady nonequilibrium

We propose and analyze a new candidate Lyapunov function for relaxation towards general nonequilibrium steady states. The proposed functional is obtained from the large time asymptotics of time-symmetric fluctuations. For driven Markov jump or diffusion processes it measures an excess in dynamical activity rates. We present numerical evidence and we report on a rigorous argument for its monotonous time-dependence close to the steady nonequilibrium or in general after a long enough time. This is in contrast with the behavior of approximate Lyapunov functions based on entropy production that when driven far from equilibrium often keep exhibiting temporal oscillations even close to stationarity.Comment: Accepted for publication in Phys. Rev. Let

Steady state statistics of driven diffusions

We consider overdamped diffusion processes driven out of thermal equilibrium and we analyze their dynamical steady fluctuations. We discuss the thermodynamic interpretation of the joint fluctuations of occupation times and currents; they incorporate respectively the time-symmetric and the time-antisymmetric sector of the fluctuations. We highlight the canonical structure of the joint fluctuations. The novel concept of traffic complements the entropy production for the study of the occupation statistics. We explain how the occupation and current fluctuations get mutually coupled out of equilibrium. Their decoupling close-to-equilibrium explains the validity of entropy production principles.Comment: rewritten versio