Response and flux of information in extended non-equilibrium dynamics

It is well known that entropy production is a proxy to the detection of non-equilibrium, i.e. of the absence of detailed balance, in stochastic processes and physical models; 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, for instance, by studying transfer entropy and response, which allow to quantify the relative influence of parts of the system and the asymmetry of the fluxes.

In order to understand the connection 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 also include nonlinear terms to the dynamics. Extensive numerical investigation of these models 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 model (1996) for Earth oceanic circulation.