Manifest and Subtle Cyclic Behavior in Nonequilibrium Steady States

TL;DR

This paper develops a theoretical framework to analyze cyclic behaviors in nonequilibrium steady states of stochastic systems, introducing probability angular momentum to distinguish manifest and subtle cyclic phenomena.

Contribution

It introduces the concept of probability angular momentum and its distribution to analyze cyclic behavior in NESS, with applications to climate system variability.

Findings

Cyclic behavior in NESS can be manifest or subtle.

Probability angular momentum effectively characterizes cyclic phenomena.

Application to climate data reveals underlying NESS properties.

Abstract

Many interesting phenomena in nature are described by stochastic processes with irreversible dynamics. To model these phenomena, we focus on a master equation or a Fokker-Planck equation with rates which violate detailed balance. When the system settles in a stationary state, it will be a nonequilibrium steady state (NESS), with time independent probability distribution as well as persistent probability current loops. The observable consequences of the latter are explored. In particular, cyclic behavior of some form must be present: some are prominent and manifest, while others are more obscure and subtle. We present a theoretical framework to analyze such properties, introducing the notion of "probability angular momentum" and its distribution. Using several examples, we illustrate the manifest and subtle categories and how best to distinguish between them. These techniques can be applied to reveal the NESS nature of a wide range of systems in a large variety of areas. We illustrate with one application: variability of ocean heat content in our climate system.