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

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.