Gammalike mass distributions and mass fluctuations in conserved-mass transport processes
arXiv:1306.5591 · doi:10.1103/PhysRevLett.112.030601
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 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 subsystem mass in these models is proportional to 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.
arXiv comment5 pages, 1 figure
References in corpus (18)
- Statistical Physics of Vehicular Traffic and Some Related Systems
- Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
- Colloquium: Statistical mechanics of money, wealth, and income
- A Model for Force Fluctuations in Bead Packs
- Statistical mechanics of money: How saving propensity affects its distribution
- A statistical model with a standard Gamma distribution
- Nonequilibrium Phase Transitions in Models of Aggregation, Adsorption, and Dissociation
- Factorised Steady States in Mass Transport Models
- Interaction driven real-space condensation
- Asymmetric particle systems on R
- Generic features of the wealth distribution in ideal-gas-like markets
- Definition and relevance of nonequilibrium intensive thermodynamic parameters
- Intensive thermodynamic parameters in nonequilibrium systems
- Approximate thermodynamic structure for driven lattice gases in contact
- Temperature in nonequilibrium systems with conserved energy
- Nonequilibrium steady states in contact: Approximate thermodynamic structure and zero-th law for driven lattice gases
- Matrix product approach for the asymmetric random average process
- Conserved mass models with stickiness and chipping
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