  We show that the equations which describe irreversible evolution of a system
can be derived from a variational principle. We suggest a Lagrangian, which
depends on the properties of the normal and the so-called "mirror-image"
system. The Lagrangian is symmetric in time and therefore compatible with
microscopic reversibility. The evolution equations in the normal and
mirror-imaged systems are decoupled and describe therefore independent
irreversible evolution of each of the systems. The second law of thermodynamics
follows from a symmetry of the Lagrangian. Entropy increase in the normal
system is balanced by the entropy decrease in the mirror-image system, such
that there exist an "integral of evolution" which is a constant. The derivation
relies on the property of local equilibrium, which states that the local
relations between the thermodynamic quantities in non-equilibrium are the same
as in equilibrium.
