Dissipation Function: Nonequilibrium Physics and Dynamical Systems

An exact response theory has recently been developed within the field of Nonequilibrium Molecular Dynamics. Its main ingredient is known as the Dissipation Function, <inline-formula><math display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula>. This quantity determines nonequilbrium properties like thermodynamic potentials do with equilibrium states. In particular, <inline-formula><math display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula> can be used to determine the exact response of particle systems obeying classical mechanical laws, subjected to perturbations of arbitrary size. Under certain conditions, it can also be used to express the response of a single system, in contrast to the standard response theory, which concerns ensembles of identical systems. The dimensions of <inline-formula><math display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula> are those of a rate, hence <inline-formula><math display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula> can be associated with the entropy production rate, provided local thermodynamic equilibrium holds. When this is not the case for a particle system, or generic dynamical systems are considered, <inline-formula><math display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula> can equally be defined, and it yields formal, thermodynamic-like, relations. While such relations may have no physical content, they may still constitute interesting characterizations of the relevant dynamics. Moreover, such a formal approach turns physically relevant, because it allows a deeper analysis of <inline-formula><math display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula> and of response theory than possible in case of fully fledged physical models. Here, we investigate the relation between linear and exact response, pointing out conditions for the validity of the response theory, as well as difficulties and opportunities for the physical interpretation of certain formal results.