Time Reversal Invariance of quantum kinetic equations: Nonequilibrium Green Functions Formalism

Time reversal symmetry is a fundamental property of many quantum mechanical systems. The relation between statistical physics and time reversal is subtle and not all statistical theories conserve this particular symmetry, most notably hydrodynamic equations and kinetic equations such as the Boltzmann equation. In this article it is shown analytically that quantum kinetic generalizations of the Boltzmann equation that are derived using the nonequilibrium Green functions formalism as well as all approximations that stem from $\mathrm{\Phi }$-derivable selfenergies are time reversal invariant.