Variational principle for theories with dissipation from analytic continuation

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.

34 pages, improved discussion of dissipative terms in energy momentum tensor, references added

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• Linear response theory of relativistic hydrodynamics with spin
• Effective Action for Relativistic Hydrodynamics: Fluctuations, Dissipation, and Entropy Inflow
• Global Anomalies, Discrete Symmetries, and Hydrodynamic Effective Actions
• Transport and hydrodynamics in the chiral limit
• Thermodynamics from relative entropy
• Renormalization-group flow of the effective action of cosmological large-scale structures
• Second law of thermodynamics for relativistic fluids formulated with relative entropy
• Spatial entanglement in interacting Bose-Einstein condensates
• Conserved and non-conserved Noether currents from the quantum effective action
• Electrical conductivity of the quark-gluon plasma from the low energy limit of photon and dilepton spectra
• Action Functional for a Particle with Damping
• Functional Renormalization Analytically Continued