Current fluctuations in stochastic systems with long-range memory

2009/04/30 by R. J. Harris, R J Harris, H. Touchette +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analogy #Class (philosophy) #Current (fluid) #Function (biology) #Large deviations theory #Particle system #Stochastic process #Stochastic processes and statistical mechanics #cond-mat.stat-mech #stochastic dynamics and bifurcation

paper · pdf · doi:10.1088/1751-8113/42/34/342001

published as J. Phys. A: Math. Theor. 42 (2009) 342001 · 10 pages, 1 figure. v2: Minor alterations. v3: Very minor alterations for consistency with published version appearing at http://stacks.iop.org/1751-8121/42/342001

openalex publication_date 2009/08/06 · arxiv created 2009/08/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We propose a method to calculate the large deviations of current fluctuations in a class of stochastic particle systems with history-dependent rates. Long-range temporal correlations are seen to alter the speed of the large deviation function in analogy with long-range spatial correlations in equilibrium systems. We give some illuminating examples and discuss the applicability of the Gallavotti–Cohen fluctuation theorem.

Citations

• Current Large Deviations for Asymmetric Exclusion Processes with Open Boundaries
• Phase transition in random walks with long-range correlations
• On the range of validity of the fluctuation theorem for stochastic Markovian dynamics
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Exact moments in a continuous time random walk with complete memory of its history
• Mathematical Biology

Cited by

• Anomalous Scaling of Dynamical Large Deviations
• Fluctuation relations without uniform large deviations
• Quantum walks with memory provided by recycled coins and a memory of the coin-flip history