  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. Whereas the total entropy of system plus reservoirs is conserved,
we show that the system entropy production is always positive and is a direct
measure of the 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 system and 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.
