Probability of a single current

Abstract

The Riemann surface associated with counting the current between two states of an underlying Markov process is hyperelliptic. We explore the consequences of this property for the time-dependent probability of that current for Markov processes with generic transition rates. When the system is prepared in its stationary state, the relevant meromorphic differential is in particular fully characterized by the precise identification of all its poles and zeroes.

arXiv comment39 pages

References in corpus (9)

• The large deviation approach to statistical mechanics
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• The physics of exceptional points
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Fluctuation theorems for stochastic dynamics
• Excited states by analytic continuation of TBA equations
• Riemann surface for TASEP with periodic boundaries
• Riemann surfaces for integer counting processes