Current fluctuations in nonequilibrium discontinuous phase transitions

TL;DR

This paper investigates the fluctuations of thermodynamic currents during nonequilibrium discontinuous phase transitions, emphasizing the role of metastability lifetime and introducing conditional currents analyzed through large deviation theory.

Contribution

It introduces the concept of conditional currents and explores their fluctuation behavior, connecting them to average currents and variances in the context of nonequilibrium phase transitions.

Findings

Conditional currents relate to average and variance via finite-time Large Deviation Theory.

Metastability lifetime significantly influences fluctuation behavior.

Results validated in chemical reaction and Potts model simulations.

Abstract

Discontinuous phase transitions out of equilibrium can be characterized by the behavior of macroscopic stochastic currents. But while much is known about the the average current, the situation is much less understood for higher statistics. In this paper, we address the consequences of the diverging metastability lifetime -- a hallmark of discontinuous transitions -- in the fluctuations of arbitrary thermodynamic currents, including the entropy production. In particular, we center our discussion on the \emph{conditional} statistics, given which phase the system is in. We highlight the interplay between integration window and metastability lifetime, which is not manifested in the average current, but strongly influences the fluctuations. We introduce conditional currents and find, among other predictions, their connection to average and scaled variance through a finite-time version of Large Deviation Theory and a minimal model. Our results are then further verified in two paradigmatic models of discontinuous transitions: Schl\"ogl's model of chemical reactions, and a $12$-states Potts model subject to two baths at different temperatures.