Non-Equilibrium 2PI Potential and Its Possible Application to Evaluation of Bulk Viscosity

TL;DR

This paper introduces a non-equilibrium potential within the 2PI Green's function framework, which generalizes thermodynamic potential and offers a new method to evaluate bulk viscosity in non-equilibrium systems.

Contribution

It develops a non-equilibrium potential based on the 2PI $ extit{ ext{Φ}}$-functional method that extends thermodynamic concepts to non-equilibrium states and links volume variations to bulk viscosity.

Findings

Non-equilibrium potential coincides with thermodynamic potential at equilibrium.

Variation of the potential relates to the non-equilibrium stress tensor.

Provides a novel approach for bulk viscosity evaluation.

Abstract

Within non-equilibrium Green's function technique on the real-time contour and the two-particle-irreducable (2PI) $\Phi$-functional method, a non-equilibrium potential is introduced. It naturally generalizes the conventional thermodynamic potential with which it coincides in thermal equilibrium. Variations of the non-equilibrium potential over respective parameters result in the same quantities as those of the thermodynamic potential but in arbitrary non-equilibrium. In particular, for slightly non-equilibrium inhomogeneous configurations a variation of the non-equilibrium potential over volume is associated with the trace of the non-equilibrium stress tensor. The latter is related to the bulk viscosity. This provides a novel way for evaluation of the bulk viscosity.