This paper was written by Roderick Dewar and published in 2005. In this paper and another he published two years earlier (2003), 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 of this article states: “Recently the author used an information theoretical formulation of non-equilibrium statistical mechanics (MaxEnt) to derive the fluctuation theorem (FT) concerning the probability of second law violating phase-space paths. A less rigorous argument leading to the variational principle of maximum entropy production (MEP) was also given. Here a more rigorous and general mathematical derivation of MEP from MaxEnt is presented, and the relationship between MEP and the FT is thereby clarified. Specifically, it is shown that the FT allows a general orthogonality property of maximum information entropy to be extended to entropy production itself, from which MEP then follows. The new derivation highlights MEP and the FT as generic properties of MaxEnt probability distributions involving anti-symmetric constraints, independently of any physical interpretation. Physically, MEP applies to the entropy production of those macroscopic fluxes that are free to vary under the imposed constraints, and corresponds to selection of the most probable macroscopic flux configuration. In special cases MaxEnt also leads to various upper bound transport principles. The relationship between MaxEnt and previous theories of irreversible processes due to Onsager, Prigogine and Ziegler is also clarified in the light of these results.”
Dewar, R. 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)
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)