Entropy production as correlation between system and reservoir

We derive an exact (classical and quantum) expression for the
entropy production of a finite system placed in contact with one or several
finite reservoirs, each of which is initially described by a canonical equilibrium
distribution. Although the total entropy of system plus reservoirs is conserved,
we show that system entropy production is always positive and is a direct
measure of system–reservoir correlations and/or entanglements. Using an
exactly solvable quantum model, we illustrate our novel interpretation of the
Second Law in a microscopically reversible finite-size setting, with strong
coupling between the system and the reservoirs. With this model, we also
explicitly show the approach of our exact formulation to the standard description
of irreversibility in the limit of a large reservoir.