Extended Keldysh formalism for entropy evaluation

The Keldysh formalism is a key approach for calculating Green's functions out of equilibrium. We present a scheme to utilize the main part of the formalism, the closed time contour, for entropy production calculations in open quantum systems. To this end, we apply the formalism not to Green's functions, but to density matrices. By extending the Keldysh contour to multiple connected contours for copies of the density matrix, we use it to represent flows of Rényi entropies, and determine symmetries in perturbative calculations. This scheme is applied to simplify calculations of von Neumann entropy production.