arXiv subjects

Vivien Lecomte

Publications and source records attributed to Vivien Lecomte.

63 records · Page 4Linked to original sources

arXiv2008

Mapping out of equilibrium into equilibrium in one-dimensional transport models

Systems with conserved currents driven by reservoirs at the boundaries offer an opportunity for a general analytic study that is unparalleled in more general out of equilibrium systems. The evolution of coarse-grained variables is governed by stochastic {\em hydrodynamic} equations in the limit of small noise.} As such it is amenable to a treatment formally equal to the semiclassical limit of quantum mechanics, which reduces the problem of finding the full distribution functions to the solution of a set of Hamiltonian equations. It is in general not possible to solve such equations explicitly, but for an interesting set of problems (driven Symmetric Exclusion Process and Kipnis-Marchioro-Presutti model) it can be done by a sequence of remarkable changes of variables. We show that at the bottom of this `miracle' is the surprising fact that these models can be taken through a non-local transformation into isolated systems satisfying detailed balance, with probability distribution given by the Gibbs-Boltzmann measure. This procedure can in fact also be used to obtain an elegant solution of the much simpler problem of non-interacting particles diffusing in a one-dimensional potential, again using a transformation that maps the driven problem into an undriven one.

cond-mat.stat-mech↗

arXiv2008

Universal cumulants of the current in diffusive systems on a ring

We calculate exactly the first cumulants of the integrated current and of the activity (which is the total number of changes of configurations) of the symmetric simple exclusion process (SSEP) on a ring with periodic boundary conditions. Our results indicate that for large system sizes the large deviation functions of the current and of the activity take a universal scaling form, with the same scaling function for both quantities. This scaling function can be understood either by an analysis of Bethe ansatz equations or in terms of a theory based on fluctuating hydrodynamics or on the macroscopic fluctuation theory of Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim.

cond-mat.stat-mech↗

arXiv2007

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.

cond-mat.stat-mech↗

arXiv2007

Thermodynamic formalism and large deviation functions in continuous time Markov dynamics

The thermodynamic formalism, which was first developed for dynamical systems and then applied to discrete Markov processes, turns out to be well suited for continuous time Markov processes as well, provided the definitions are interpreted in an appropriate way. Besides, it can be reformulated in terms of the generating function of an observable, and then extended to other observables. In particular, the simple observable $K$ giving the number of events occurring over a given time interval turns out to contain already the signature of dynamical phase transitions. For mean-field models in equilibrium, and in the limit of large systems, the formalism is rather simple to apply and shows how thermodynamic phase transitions may modify the dynamical properties of the systems. This is exemplified with the q-state mean-field Potts model, for which the Ising limit q=2 is found to be qualitatively different from the other cases.

cond-mat.stat-mech↗

arXiv2007

Current distribution in systems with anomalous diffusion: renormalisation group approach

We investigate the asymptotic properties of the large deviation function of the integrated particle current in systems, in or out of thermal equilibrium, whose dynamics exhibits anomalous diffusion. The physical systems covered by our study include mutually repelling particles with a drift, a driven lattice gas displaying a continuous nonequilibrium phase transition, and particles diffusing in a anisotropic random advective field. It is exemplified how renormalisation group techniques allow for a systematic determination of power laws in the corresponding current large deviation functions. We show that the latter are governed by known universal scaling exponents, specifically, the anomalous dimension of the noise correlators.

cond-mat.stat-mech↗

arXiv2007

A numerical approach to large deviations in continuous-time

We present an algorithm to evaluate the large deviation functions associated to history-dependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm, valuable for systems with multiple time scales, thus extending the work of Giardinà, Kurchan and Peliti (PRL 96, 120603 (2006)). The procedure is supplemented with a thermodynamic-integration scheme, which improves its efficiency. We also show how the method can be used to probe large deviation functions in systems with a dynamical phase transition -- revealed in our context through the appearance of a non-analyticity in the large deviation functions.

cond-mat.stat-mech↗

arXiv2006

Thermodynamic formalism for systems with Markov dynamics

The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time. We also generalize the formalism --a dynamical Gibbs ensemble construction-- to a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the much-studied fluctuation theorem. We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unravelled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window.

cond-mat.stat-mech↗

arXiv2005

Chaotic properties of systems with Markov dynamics

We present a general approach for computing the dynamic partition function of a continuous-time Markov process. The Ruelle topological pressure is identified with the large deviation function of a physical observable. We construct for the first time a corresponding finite Kolmogorov-Sinai entropy for these processes. Then, as an example, the latter is computed for a symmetric exclusion process. We further present the first exact calculation of the topological pressure for an N-body stochastic interacting system, namely an infinite-range Ising model endowed with spin-flip dynamics. Expressions for the Kolmogorov-Sinai and the topological entropies follow.

cond-mat.stat-mech↗

arXiv2004

Energy flux distribution in a two-temperature Ising model

The nonequilibrium steady state of an infinite-range Ising model is studied. The steady state is obtained by dividing the spins into two groups and attaching them to two heat baths generating spin flips at different temperatures. In the thermodynamic limit, the resulting dynamics can be solved exactly, and the probability flow in the phase space can be visualized. We can calculate the steady state fluctuations far from equilibrium and, in particular, we find the exact probability distribution of the energy current in both the high- and low-temperature phase.

cond-mat.stat-mech↗