Analytic study of the three-urn model for separation of sand
arXiv:cond-mat/0402113 · doi:10.1103/PhysRevE.70.031305
Abstract
We present an analytic study of the three-urn model for separation of sand. We solve analytically the master equation and the first-passage problem. We find that the stationary probability distribution obeys the detailed balance and is governed by the {\it free energy}. We find that the characteristic lifetime of a cluster diverges algebraically with exponent 1/3 at the limit of stability.
arXiv comment5pages, 4 figures included
References in corpus (9)
- Phase Transitions in one-dimensional nonequilibrium systems
- Sand as Maxwell's demon
- Condensation in the zero range process: stationary and dynamical properties
- Sudden Collapse of a Granular Cluster
- Urn model of separation of sand
- Dynamics of a disordered, driven zero range process in one dimension
- Dynamics of the breakdown of granular clusters
- Yang-Lee zeroes for an urn model for the separation of sand
- Analytic study of the urn model for separation of sand
Cited by in corpus (10)
- Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
- Current fluctuations in the zero-range process with open boundaries
- Zero-range process with open boundaries
- Breakdown of Gallavotti-Cohen symmetry for stochastic dynamics
- On the range of validity of the fluctuation theorem for stochastic Markovian dynamics
- Analytic study of clustering in shaken granular material using zero-range processes
- Hydrodynamics of the zero-range process in the condensation regime
- Local structure of current fluctuations in diffusive systems beyond one dimension
- Non-equilibrium thermodynamics and Phase transition of Ehrenfest urns with interactions
- Dynamics of condensate formation in stochastic transport with pair-factorized steady states: Nucleation and coarsening time scales