Ju l 2 00 8 An Explicit Microreversibility Violating Thermodynamic Markov Process

The practice of statistical physics often involves Monte Carlo studies of model thermodynamic systems such as the Ising spin-lattice [1, 2, 3] and the Potts model [4, 5]. These studies are normally conducted with a Markov process that takes a random walk through the space of all allowed system configurations, producing a chain of states in which each individual state appears with a frequency proportional to its Gibbs probability [6]. Such a Markov process must satisfy two conditions. The first of these is the accessibility criterion, that from any given initial state it must be possible to evolve the system, given sufficient time, into any other possible state. This is equivalent to the physical property of ergodicity. The second requirement, in order for the equilibrium Gibbs ensemble to exist, is that the state-to-state transition probabilities of the Markov process must satisfy the invariance condition