arXiv subjects

Raphael Chetrite

Publications and source records attributed to Raphael Chetrite.

30 records · Page 2Linked to original sources

arXiv2012

A Gallavotti-Cohen-Evans-Morriss like symmetry for a class of Markov jump processes

We investigate a new symmetry of the large deviation function of certain time-integrated currents in non-equilibrium systems. The symmetry is similar to the well-known Gallavotti-Cohen-Evans-Morriss-symmetry for the entropy production, but it concerns a different functional of the stochatic trajectory. The symmetry can be found in a restricted class of Markov jump processes, where the network of microscopic transitions has a particular structure and the transition rates satisfy certain constraints. We provide three physical examples, where time-integrated observables display such a symmetry. Moreover, we argue that the origin of the symmetry can be traced back to time-reversal if stochastic trajectories are grouped appropriately.

cond-mat.stat-mech↗

arXiv2011

Quantum Fluctuation Relations for the Lindblad Master Equation

An open quantum system interacting with its environment can be modeled under suitable assumptions as a Markov process, described by a Lindblad master equation. In this work, we derive a general set of fluctuation relations for systems governed by a Lindblad equation. These identities provide quantum versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula.

cond-mat.stat-mech↗

arXiv2011

Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale

In the context of Markov evolution, we present two original approaches to obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the language of stochastic derivatives and by using a family of exponential martingales functionals. We show that GFDT are perturbative versions of relations verified by these exponential martingales. Along the way, we prove GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the usual proof for diffusion and pure jump processes. Finally, we relate the FR to a family of backward and forward exponential martingales.

cond-mat.stat-mech↗

arXiv2010

Fluctuation Relations for Quantum Markovian Dynamical System

We derive a general set of fluctuation relations for a nonequilibrium open quantum system described by a Lindblad master equation. In the special case of conservative Hamiltonian dynamics, these identities allow us to retrieve quantum versions of Jarzynski and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula.

cond-mat.stat-mech↗

arXiv2009

Fluctuation Relations for Diffusions Thermally Driven by a Non-Stationnary Bath

In the context of the dynamical evolution in a non-stationary thermal bath, we construct a family of fluctuation relations for the entropy production that are not verified by the work performed on the system. We exhibit fluctuation relations which are global versions either of the generalized Fluctuation-Dissipation Theorem around a non-equilibrium diffusion or of the usual Fluctuation-Dissipation Theorem for energy resulting from a pulse of temperature.

cond-mat.stat-mech↗

arXiv2009

Experimental verification of a modified fluctuation-dissipation relation for a micron-sized particle in a non-equilibrium steady state

A modified fluctuation-dissipation-theorem (MFDT) for a non-equilibrium steady state (NESS) is experimentally checked by studying the position fluctuations of a colloidal particle whose motion is confined in a toroidal optical trap. The NESS is generated by means of a rotating laser beam which exerts on the particle a sinusoidal conservative force plus a constant non-conservative one. The MFDT is shown to be perfectly verified by the experimental data. It can be interpreted as an equilibrium-like fluctuation-dissipation relation in the Lagrangian frame of the mean local velocity of the particle.

cond-mat.stat-mech↗

arXiv2009

Eulerian and Lagrangian pictures of non-equilibrium diffusions

We show that a non-equilibrium diffusive dynamics in a finite-dimensional space takes in the Lagrangian frame of its mean local velocity an equilibrium form with the detailed balance property. This explains the equilibrium nature of the fluctuation-dissipation relations in that frame observed previously. The general considerations are illustrated on few examples of stochastic particle dynamics.

cond-mat.stat-mech↗

arXiv2008

Fluctuations relations for semiclassical single-mode laser

Over last decades, the study of laser fluctuations has shown that laser theory may be regarded as a prototypical example of a nonlinear nonequilibrium problem. The present paper discusses the fluctuation relations, recently derived in nonequilibrium statistical mechanics, in the context of the semiclassical laser theory.

cond-mat.stat-mech↗

arXiv2008

Fluctuation relations in simple examples of non-equilibrium steady states

We discuss fluctuation relations in simple cases of non-equilibrium Langevin dynamics. In particular, we show that close to non-equilibrium steady states with non-vanishing probability currents some of these relations reduce to a modified version of the fluctuation-dissipation theorem. The latter may be interpreted as the equilibrium-like relation in the reference frame moving with the mean local velocity determined by the probability current.

cond-mat.stat-mech↗

arXiv2007

Fluctuation Relations for Diffusion Processes

The paper presents a unified approach to different fluctuation relations for classical nonequilibrium dynamics described by diffusion processes. Such relations compare the statistics of fluctuations of the entropy production or work in the original process to the similar statistics in the time-reversed process. The origin of a variety of fluctuation relations is traced to the use of different time reversals. It is also shown how the application of the presented approach to the tangent process describing the joint evolution of infinitesimally close trajectories of the original process leads to a multiplicative extension of the fluctuation relations.

math-ph↗

arXiv2007

Toward a phenomenological approach to the clustering of heavy particles in turbulent flows

A simple model accounting for the ejection of heavy particles from the vortical structures of a turbulent flow is introduced. This model involves a space and time discretization of the dynamics and depends on only two parameters: the fraction of space-time occupied by rotating structures of the carrier flow and the rate at which particles are ejected from them. The latter can be heuristically related to the response time of the particles and hence measure their inertia. It is shown that such a model reproduces qualitatively most aspects of the spatial distribution of heavy particles transported by realistic flows. In particular the probability density function of the mass $m$ in a cell displays an power-law behavior at small values and decreases faster than exponentially at large values. The dependence of the exponent of the first tail upon the parameters of the dynamics is explicitly derived for the model. The right tail is shown to decrease as $\exp (-C m \log m)$. Finally, the distribution of mass averaged over several cells is shown to obey rescaling properties as a function of the coarse-grain size and of the ejection rate of the particles. Contrarily to what has been observed in direct numerical simulations of turbulent flows (Bec et al., http://arxiv.org/nlin.CD/0608045), such rescaling properties are only due in the model to the mass dynamics of the particles and do not involve any scaling properties in the spatial structure of the carrier flow.

nlin.CD↗

arXiv2006

Kraichnan flow in a square: an example of integrable chaos

The Kraichnan flow provides an example of a random dynamical system accessible to an exact analysis. We study the evolution of the infinitesimal separation between two Lagrangian trajectories of the flow. Its long-time asymptotics is reflected in the multiplicative large deviation regime of the statistics of stretching exponents. In the flow in a two-dimensional periodic square where the anisotropy persists at small scales, the calculation of the large deviation rate function of the stretching exponents reduces to the study of the ground state energy of an integrable periodic Schroedinger operator of the Lame type. The underlying integrability permits to explicitly exhibit the non-Gaussianity of the multiplicative large deviations, to analyze the time-scales at which the large deviation regime sets in and to identify the general scenario for the appearance of multiplicative large deviations and the restrictions on its applicability.

nlin.CD↗