Variational principle for theories with dissipation from analytic continuation

Understand

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.