Derivation of irreversibility of thermodynamic processes from microscopic reversibility

Under the assumption that the random internal thermodynamic parameters $B_\alpha(t)$ are the components of a reversible Markov process it is shown that the change in the free energy $\Psi(A)$, where $A_\alpha=\langle B_\alpha\rangle$ are nonequilibrium mean values, is irreversible. The methods of Markovian nonlinear nonequilibrium thermodynamics are used.