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.
Highlights
In the standard Boltzmann-Gibbs formulation of equilibrium statistical mechanics, time plays no role
Summary and Outlook We have shown that the angular momenta L∗ and the two point correlation at unequal times C ∗ (τ ) are, for any non-equilibrium steady states (NESS), excellent measures of the underlying time-reversal and detailed balance (DB) violating dynamics
Any multipoint correlation functions at unequal times will provide a platform for measuring such characteristics
Summary
- Nonequilibrium meson production in strong fields L Juchnowski, D Blaschke, T Fischer et al. - Thermodynamics and phase coexistence in nonequilibrium steady states Ronald Dickman. - Nonequilibrium carrier dynamics in ultrathin Si-on-glass films J Serafini, Y Akbas, L Crandall et al
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