Exponential peak and scaling of work fluctuations in modulated systems

TL;DR

This paper extends the work fluctuation theorem to nonlinear systems with periodic modulation, revealing sharp increases in work fluctuations near phase transitions and bifurcation points, with specific scaling laws.

Contribution

It introduces a generalized fluctuation theorem for modulated nonlinear systems and characterizes the scaling behavior of work fluctuations near critical points.

Findings

Work fluctuations sharply increase near kinetic phase transitions.

Work variance is proportional to the reciprocal of interstate switching rate.

Variance scales with the distance to a bifurcation point, with a specific critical exponent.

Abstract

We extend the stationary-state work fluctuation theorem to periodically modulated nonlinear systems. Such systems often have coexisting stable periodic states. We show that work fluctuations sharply increase near a kinetic phase transition where the state populations are close to each other. The work variance is proportional here to the reciprocal rate of interstate switching. We also show that the variance displays scaling with the distance to a bifurcation point and find the critical exponent for a saddle-node bifurcation.