Gradient structure and transport coefficients for strong particles

Abstract

We introduce and study a simple and natural class of solvable stochastic lattice gases. This is the class of Strong Particles. The name is due to the fact that when they try to jump to an occupied site they succeed pushing away a pile of particles. For this class of models we explicitly compute the transport coefficients. We also discuss some generalizations and the relations with other classes of solvable models.

Reply to “Comment on ‘Generalized exclusion processes: Transport coefficients’ ”

“…Generally for lattice gases even with rather simple hopping rules, analytic results are unattainable; however, when an additional feature, known as the gradient condition, is satisfied, the Green-Kubo formula takes a simple form [3] and computations of the transport coefficients become feasible. For a number of lattice gases of gradient type, e.g., for the Katz-Lebowitz-Spohn model with symmetric hopping [4], for repulsion processes [5], for a lattice gas of leap-frogging particles [6,7], the diffusion coefficient has been rigorously computed. The gradient property is also true for the misanthrope process, a class of generalized exclusion processes [8,9].…”

Einstein’s fluctuation relation and Gibbs states far from equilibrium

“…This relation involves a non-equilibrium free energy which is maximised at stationarity, and whose corresponding entropy drives the diffusion, but does not seem to have all the properties of its equilibrium equivalent such as monotonicity. Examples of models where our results apply include many versions of exclusion processes (with interactions [8], higher occupancies [21], several types of particles [20], longer jumps [22], or longer-range exclusion [23]), as well as asymmetric versions of the inclusion process [24,25], the KMP model for heat conduction [26], and other models designed to have Gibbs stationary states [10,11].…”

Solitons in fluctuating hydrodynamics of diffusive processes

“…Although in this paper we studied in detail the SEP and KMP systems, our methods, and in particular equation (51), are completely general and work for any D(ρ) and σ(ρ). There are other instances in the literature where general results can be derived for arbitrary transport coefficients, such as, e.g., [26,27]. In particular, if D(ρ) = 1 and σ(ρ) is a quadratic polynomial, the effective potential W (ρ) is quartic.…”