4 Maximum Entropy Production and Non-equilibrium Statistical Mechanics

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Over the last 30 years empirical evidence in favour of the Maximum Entropy Production (MEP) principle for non-equilibrium systems has been accumulating from studies of phenomena as diverse as planetary climates, crystal growth morphology, bacterial metabolism and photosynthesis. And yet MEP is still regarded by many as nothing other than a curiosity, largely because a theoretical justification for it has been lacking. This chapter offers a non-mathematical overview of a recent statistical explanation of MEP stemming from the work of Boltzmann, Gibbs, Shannon and Jaynes. The aim here is to highlight the key physical ideas underlying MEP. For non-equilibrium systems that exchange energy and matter with their surroundings and on which various constraints are imposed (e.g., external forcings, conservation laws), it is shown that, among all the possible steady states compatible with the imposed constraints, Nature selects the MEP state because it is the most probable one, i.e., it is the macroscopic state that could be realised by more microscopic pathways than any other. That entropy production is the extremal quantity emerges here from the universal constraints of local energy and mass balance that apply to all systems, which may explain the apparent prevalence of MEP throughout physics and biology. The same physical ideas also explain self-organized criticality and a result concerning the probability of violations of the second law of thermodynamics (the Fluctuation Theorem), recently verified experimentally. In the light of these results, dissipative structures of high entropy production, which include living systems, can be viewed as highly probable phenomena. The prospects for applying these results to other types of non-equilibrium system, such as economies, are briefly outlined.