  In 1965 Jaynes provided an intuitively simple proof of the 2nd law of
thermodynamics as a general requirement for any macroscopic transition to be
experimentally reproducible. His proof was based on Boltzmann's formula S =
klnW and the dynamical invariance of the phase volume W for isolated systems
(Liouville's theorem). Here Jaynes' proof is extended to show that Liouville's
theorem also implies maximum entropy production (MaxEP) for the stationary
states of open, non-equilibrium systems. According to this proof, MaxEP
stationary states are selected because they can exist within a greater number
of environments than any other stationary states. Liouville's theorem applied
to isolated systems also gives an intuitive derivation of the fluctuation
theorem in a form consistent with an earlier conjecture by Jaynes on the
probability of violations of the 2nd law. The present proof of MaxEP, while
largely heuristic, suggests an approach to establishing a more fundamental
basis for MaxEP using Jaynes' maximum entropy formulation of statistical
mechanics.
