Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states

Jaynes' information theory formalism of statistical mechanics is applied to the stationary states of open, non-equilibrium systems. First, it is shown that the probability distribution pΓ of the underlying microscopic phase space trajectories Γ over a time interval of length τ satisfies pΓ ∝ exp(τσΓ/2kB) where σΓ is the time-averaged rate of entropy production of Γ. Three consequences of this result are then derived: (1) the fluctuation theorem, which describes the exponentially declining probability of deviations from the second law of thermodynamics as τ → ∞; (2) the selection principle of maximum entropy production for non-equilibrium stationary states, empirical support for which has been found in studies of phenomena as diverse as the Earth's climate and crystal growth morphology; and (3) the emergence of self-organized criticality for flux-driven systems in the slowly-driven limit. The explanation of these results on general information theoretic grounds underlines their relevance to a broad class of stationary, non-equilibrium systems. In turn, the accumulating empirical evidence for these results lends support to Jaynes' formalism as a common predictive framework for equilibrium and non-equilibrium statistical mechanics.