Stochastic pump effect and geometric phases in dissipative and stochastic systems

TL;DR

This paper explores geometric phases in classical dissipative stochastic systems and their role in the stochastic pump effect, extending concepts from quantum mechanics to stochastic environments like molecular motors.

Contribution

It introduces the concept of geometric phases in classical stochastic systems and analyzes their influence on the stochastic pump effect, bridging quantum ideas with classical stochastic dynamics.

Findings

Geometric phases can occur in classical dissipative stochastic systems.

These phases influence the behavior of the stochastic pump effect.

The study extends the understanding of geometric effects beyond quantum systems.

Abstract

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).