This paper was written by Roderick Dewar and published in 2003. In this paper and another published two years later (2005), Dewar provides a theoretical basis for the maximum entropy production principle and derives a provisional proof of it for non-equilibrium, steady-state systems, both biotic and abiotic.
The abstract for this paper 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.”
Dewar, R. 2003. Information theory explanation of the fluctuation theorem, maximum entropy production and self organized criticality in non-equilibrium stationary states. Journal of Physics A: Math and General 36: 631-641. (doi:10.1088/ 0305-4470/36/3/303)
_________. 2005. Maximum entropy production and the fluctuation theorem. Journal of Physics A: Math and General 38, L371-L381. (doi: 10.1088/0305-4470/38/21/L01)