Response and flux of information in extended non-equilibrium dynamics

TL;DR

This paper explores the relationship between entropy production, transfer entropy, and response in extended non-equilibrium systems, using analytical models and the Lorenz '96 model to reveal how information fluxes relate to entropy production.

Contribution

It introduces a comprehensive analysis linking entropy production with transfer entropy and response in spatially asymmetric non-equilibrium systems, including nonlinear dynamics.

Findings

Entropy production correlates with asymmetry in information fluxes.

Transfer entropy effectively captures influence among system components.

Application to Lorenz '96 model demonstrates practical relevance.

Abstract

It is well known that entropy production is a proxy to the detection of non-equilibrium, i.e. of the absence of detailed balance; however, due to the global character of this quantity, its knowledge does not allow to identify spatial currents or fluxes of information among specific elements of the system under study. In this respect, much more insight can be gained by studying transfer entropy and response, which allow quantifying the relative influence of parts of the system and the asymmetry of the fluxes. In order to understand the relation between the above-mentioned quantities, we investigate spatially asymmetric extended systems. First, we consider a simplified linear stochastic model, which can be studied analytically; then, we include nonlinear terms in the dynamics. Extensive numerical investigation shows the relation between entropy production and the above-introduced degrees of asymmetry. Finally, we apply our approach to the highly nontrivial dynamics generated by the Lorenz '96 model for Earth oceanic circulation.