Cycle counts and affinities in stochastic models of non-equilibrium systems

Abstract

For non-equilibrium systems described by finite Markov processes, we consider the number of times that a system traverses a cyclic sequence of states (a cycle). The joint distribution of the number of forward and backward instances of any given cycle is described by universal formulae which depend on the cycle affinity, but are otherwise independent of system details. We discuss the similarities and differences of this result to fluctuation theorems, and generalize the result to families of cycles, relevant under coarse-graining. Finally, we describe the application of large deviation theory to this cycle counting problem.

authors' accepted version

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Cited by in corpus (2)

• Entropy estimation for partially accessible Markov networks based on imperfect observations: Role of finite resolution and finite statistics
• Tight uncertainty relations for cycle currents