  We establish that entropy production, which is crucial to the
characterization of thermodynamic irreversibility, is obtained through a
variational principle involving the Kulback-Leibler divergence. A simple
application of this representation leads to an information-theoretical bound on
entropy production in thermal relaxation processes; this is a stronger
inequality than the conventional second law of thermodynamics. This bound is
also interpreted as a constraint on the possible path of a thermal relaxation
process in terms of information geometry. Our results reveal a hidden universal
law inherent to general thermal relaxation processes.
