Teoria della risposta: dissipazione e frenesia

An Exact Response Theory has recently been developed within the field of Nonequilibrium Molecular Dynamics, finding its full formalization already in the article of D. J. Evans, S. R. Williams, D. J. Searles, and L. Rondoni -- On Typicality in Nonequilibrium Steady States. Its main ingredient, which emerges from a generalized Eulerian Liouville equation, is known as the Dissipation Function $\Omega$ and it can be associated with the entropy production rate, provided local thermodynamic equilibrium holds. This quantity determines nonequilbrium properties like thermodynamic potentials do with equilibrium states. In particular, $\Omega$ can be used to determine the exact response of particle systems obeying classical mechanical laws, subjected to perturbations of arbitrary size. This theory has its origin in 1993, when Evans, Cohen and Morriss introduced the first transient fluctuation relation FR, which became popular in 1995, when Gallavotti and Cohen published the derivation of a nonequilibrium steady-state FR for an Anosov dynamical system in a well posed mathematical framework. In the last 10 years another Response Theory developed by Christian Maes and his collaborators is gaining ground. The approach is based on dynamical ensembles, determined by an action on trajectory space. (Anti)Symmetry under time-reversal separates two complementary contributions in the response, one entropic the other frenetic. Under time-reversal invariance of the unperturbed reference process, only the entropic term is present in the response, giving the standard fluctuation–dissipation relations in equilibrium. For non-equilibrium reference ensembles, the frenetic term, called Frenesy, which collects the variable quiescence and dynamical activity as function of the system’s trajectory, contributes essentially and is responsible for new phenomena. In particular, realizations for physically inspired Markov jump and diffusion processes are investigated. Both Dissipation and Frenesy lead to a Response Theory, and thus arises the need to understand how they are related, bearing in mind the fact that the first is linked to probabilities in the phase space, while the second to probabilities in the "real" space, discretized on a lattice. Dissipation and Frenesy make possible interpretations of the same phenomenon but from two different levels of reality.