The maximum entropy (MaxEnt) criterion was introduced in Statistical Mechanics by Jaynes (1957). Although it allowed for a very compact derivation of the Gibbs-Boltzmann distribution it was not widely accepted since it relied on a subjectivist view of probability, and hence was at variance with the notion that the laws of statistical mechanics are (objective) physical laws. In particular, the application of MaxEnt to non-equilibrium Statistical Mechanics has been controversial. On the other hand, maximum entropy has recently become quite popular in the context of inference. For instance, MaxEnt is, or has been claimed to be, the basis of the recently successful partial reconstruction of protein 3D structures from many homologous amino acid sequences. A recent review of MaxEnt and related theories as applied to Physics recently appeared as Presse et al (2013).
In this talk I will outline that certain simple 1D non-equilibrium statistical mechanics models investigated by Derrida and co-workers yield a counter-argument to MaxEnt in the sense that if non-equilibrium steady states of these models (which can be explicitly computed) maximize entropy with respect to some constraints, then these constraints have to be very numerous and complicated.
Part of this talk is based on a collaboration with Gino Del Ferraro and Alexander Mozeika, but nothing mentioned will be really new or independent work.
References:
Jaynes, E.T. "Information Theory and Statistical Mechanics", Physical Review vol 106, pp 620-630 (1957)
Presse S., Lee J., Dill K., "Principles of maximum entropy and maximum caliber in statistical physics", Rev Modern Physics, vol 85, pp 1115-1141 (2013)
Derrida B. "Non-equilibrium steady states: fluctuations and large deviations of the
density and of the current", JSTAT (2007) P07023
