Nonequilibrium oscillations, probability angular momentum, and the climate system

Abstract

Though the Boltzmann-Gibbs framework of equilibrium statistical mechanics has been successful in many arenas, it is clearly inadequate for describing many interesting natural phenomena driven far from equilibrium. The simplest step towards that goal is a better understanding of nonequilibrium steady-states (NESS). Here we focus on one of the distinctive features of NESS, persistent probability currents, and their manifestations in our climate system. We consider the natural variability of the steady-state climate system, which can be approximated as a NESS. These currents must form closed loops, which are odd under time reversal, providing the crucial difference between systems in thermal equilibrium and NESS. Seeking manifestations of such current loops leads us naturally to the notion of probability angular momentum and oscillations in the space of observables. Specifically, we will relate this concept to the asymmetric part of certain time-dependent correlation functions. Applying this approach, we propose that these current loops give rise to preferred spatio-temporal patterns of natural climate variability that take the form of climate oscillations such as the El-Niño Southern Oscillation (ENSO) and the Madden-Julien Oscillation (MJO). In the space of climate indices, we observe persistent currents and define a new diagnostic for these currents: the probability angular momentum. Using the observed climatic time series of ENSO and MJO, we compute both the averages and the distributions of the probability angular momentum. These results are in good agreement with the analysis from a linear Gaussian model. We propose that, in addition to being a new quantification of climate oscillations across models and observations, the probability angular momentum provides a meaningful characterization for all statistical systems in NESS.

Journal of Statistical Physics (2019)

References in corpus (10)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• On the heat flux and entropy produced by thermal fluctuations
• Mathematical and Physical Ideas for Climate Science
• Nonequilibrium and irreversibility
• Thermodynamic Efficiency and Entropy Production in the Climate System
• Characterization of the Nonequilibrium Steady State of a Heterogeneous Nonlinear $q$-Voter Model with Zealotry
• A Heterogeneous Out-of-Equilibrium Nonlinear $q$-Voter Model with Zealotry
• Experimental metrics for detection of detailed balance violation
• Exact results for a simple epidemic model on a directed network: Explorations of a system in a non-equilibrium steady state
• Macroscopically-observable probability currents in finite populations

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• Time-correlation functions for odd Langevin systems
• Irreversibility in linear systems with colored noise
• Odd elasticity of a catalytic micromachine
• Stochastic line integrals and stream functions as metrics of irreversibility and heat transfer
• Nonequilibrium Probability Currents in Optically-Driven Colloidal Suspensions
• Introduction to the Special Issue on the Statistical Mechanics of Climate
• Signals of Detailed Balance Violation in Nonequilibrium Stationary States: Subtle, Manifest, and Extraordinary