Gammalike Mass Distributions and Mass Fluctuations in Conserved-Mass Transport Processes

Abstract

We show that, in conserved-mass transport processes, the steady-state distribution of mass in a subsystem is uniquely determined from the functional dependence of variance of the subsystem mass on its mean, provided that the joint mass distribution of subsystems is factorized in the thermodynamic limit. The factorization condition is not too restrictive as it would hold in systems with short-ranged spatial correlations. To demonstrate the result, we revisit a broad class of mass transport models and its generic variants, and show that the variance of the subsystem mass in these models is proportional to the square of its mean. This particular functional form of the variance constrains the subsystem mass distribution to be a gamma distribution irrespective of the dynamical rules.

Additivity, density fluctuations, and nonequilibrium thermodynamics for active Brownian particles

“…Recently, additivity has been used in nonequilibrium mass-transport processes for calculating mass distributions and characterizing macroscopic properties in terms of equilibriumlike thermodynamic potentials [8,9]. Below, we discuss how additivity can be used to calculate subsystem particle-number distribution.…”

“…At this scenario, additivity, which originates from the simple physical consideration of statistical independence on the coarse-grained level of large subsystems, could help us to bypass the difficulty. As demonstrated recently in [8,9], to characterize fluctuation properties on a coarsegrained level, one may not actually be required to obtain the steady-state weights of all microscopic configurations. In fact, obtaining coarse-grained probability weights on a large scale (much larger than the microscopic correlation length scale) would suffice to characterize the macroscopic properties of the system, provided that additivity as in Eq.…”

“…1 holds, probability distribution function P V (N ) ≡ Prob[N k = N ] for large V can be written as [5][6][7][8],…”

“…A simple characterization of the steady-state systems in general would be certainly desirable and, to this end, various attempts have been made in the past [3,4]. Recently, a formulation based on equilibriumlike additivity property provides a framework [5][6][7], which helps one to describe a broad class of nonequilibrium steady states through fluctuations of a conserved quantity, e.g., mass or particle-number [8][9][10]. Here, we address the question whether an additivity property can be used to obtain large deviation probability for the particle-number or the density fluctuations, the central object in a statistical mechanics theory, in systems of self-propelled particles.…”

Failure of steady-state thermodynamics in nonuniform driven lattice gases

“…[3,17]. More recently, Chatterjee et al [18] established that in driven systems with particle number conservation and short-ranged correlations, fluctuations in the particle number n s of a subsystem are determined by the functional relation between the variance and the mean of n s . They argued that this guarantees the existence of a chemical potential.…”