  A quantum statistical expression for the entropy of a nonequilibrium system
is defined so as to be consistent with Gibbs' relation, and is shown to
corresponds to dynamical variable by introducing analogous to the Heisenberg
picture in quantum mechanics. The general relation between system-reservoir
interactions and an entropy change operator in an open quantum system, relying
just on the framework of statistical mechanics and the definition of von
Neumann entropy. By using this formula, we can obtain the correct entropy
production in the linear response framework. The present derivation of entropy
production is directly based on the first principle of microscopic
time-evolution, while the previous standard argument is due to the
thermodynamic energy balance.
