Discrete changes of current statistics in periodically driven stochastic systems

TL;DR

This paper reveals that the counting statistics of currents in periodically driven stochastic systems can undergo abrupt changes due to a topological phase factor, analogous to geometric phases in quantum systems, linked to degeneracy points in control parameter space.

Contribution

It introduces a topological phase factor in the evolution of the moment generating function for stochastic currents, connecting topological properties to observable statistical sign changes.

Findings

Sign change in the probability difference for even and odd particle transfer

Identification of degeneracy points in control parameter space causing sign changes

Relation between path topology and statistical properties via Stiefel-Whitney class

Abstract

We demonstrate that the counting statistics of currents in periodically driven ergodic stochastic systems can show sharp changes of some of its properties in response to continuous changes of the driving protocol. To describe this effect, we introduce a new topological phase factor in evolution of the moment generating function which is akin to the topological geometric phase in evolution of a periodically driven quantum mechanical system with time-reversal symmetry. This phase leads to the prediction of a sign change for the difference of the probabilities to find even and odd number particles transferred in a stochastic system in response to cyclic evolution of control parameters. The driving protocols that lead to such a sign change should enclose specific degeneracy points in the space of control parameters. The relation between topology of the paths in the control parameter space and the sign changes can be described in terms of the first Stiefel-Whitney class.