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.Comment: 11 pages, 3 figure

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.Comment: 16 pages, 8 figure

The number of potential winners in Bradley-Terry model in random environment

We consider a Bradley-Terry model in random environment where each player faces each other once. More precisely the strengths of the players are assumed to be random and we study the influence of their distributions on the asymptotic number of potential winners.First we prove that under mild assumptions, mainly on their moments, if the strengths are unbounded, the asymptotic probability that the best player wins is 1. We also exhibit a sufficient convexity condition to obtain the same result when the strengths are bounded. When this last condition fails, the number of potential winners grows at a rate depending on the tail of the distribution of strengths. We also study the minimal strength required for an additional player to win in this last case

Fluctuation-Dissipation Theorem in Nonequilibrium Steady States

In equilibrium, the fluctuation-dissipation theorem (FDT) expresses the response of an observable to a small perturbation by a correlation function of this variable with another one that is conjugate to the perturbation with respect to \emph{energy}. For a nonequilibrium steady state (NESS), the corresponding FDT is shown to involve in the correlation function a variable that is conjugate with respect to \emph{entropy}. By splitting up entropy production into one of the system and one of the medium, it is shown that for systems with a genuine equilibrium state the FDT of the NESS differs from its equilibrium form by an additive term involving \emph{total} entropy production. A related variant of the FDT not requiring explicit knowledge of the stationary state is particularly useful for coupled Langevin systems. The \emph{a priori} surprising freedom apparently involved in different forms of the FDT in a NESS is clarified.Comment: 6 pages; EPL, in pres

Motility-induced phase separation of active particles in the presence of velocity alignment

Self-propelled particle (SPP) systems are intrinsically out of equilibrium systems, where each individual particle converts energy into work to move in a dissipative medium. When interacting through a velocity alignment mechanism, and the medium acts as a momentum sink, even momentum is not conserved. In this scenario, a mapping into an equilibrium system seems unlikely. Here, we show that an entropy functional can be derived for SPPs with velocity alignment and density-dependent speed, at least in the (orientationally) disordered phase. This non-trivial result has important physical consequences. The study of the entropy functional reveals that the system can undergo phase separation before the orientational-order phase transition known to occur in SPP systems with velocity alignment.Moreover, we indicate that the spinodal line is a function of the alignment sensitivity and show that density fluctuations as well as the critical spatial diffusion, that leads to phase separation, dramatically increase as the orientational-order transition is approached.Comment: Published in J. Stat. Phy