Variational principle for theories with dissipation from analytic continuation

TL;DR

This paper develops a variational principle for dissipative theories by analytically continuing the quantum effective action from Euclidean to real space, enabling causal equations of motion that incorporate dissipation and entropy production.

Contribution

It introduces a generalized variational principle that accounts for dissipation via analytic continuation, extending traditional methods to include dissipative dynamics in a covariant framework.

Findings

Derivation of causal, real dissipative equations of motion

Formulation of entropy production consistent with the second law

Application to generalized local equilibrium states

Abstract

The analytic continuation from the Euclidean domain to real space of the one-particle irreducible quantum effective action is discussed in the context of generalized local equilibrium states. Discontinuous terms associated with dissipative behavior are parametrized in terms of a conveniently defined sign operator. A generalized variational principle is then formulated, which allows to obtain causal and real dissipative equations of motion from the analytically continued quantum effective action. Differential equations derived from the implications of general covariance determine the space-time evolution of the temperature and fluid velocity fields and allow for a discussion of entropy production including a local form of the second law of thermodynamics.