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 pGamma of the underlying microscopic phase space trajectories Gamma over a time interval of length tau satisfies pGamma propto exp(tausigmaGamma/2kB) where sigmaGamma is the time-averaged rate of entropy production of Gamma. 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 tau rightarrow infty; (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.
Journal of Physics A Mathematical General
- Pub Date:
- January 2003
- Condensed Matter - Statistical Mechanics;
- Physics - Atmospheric and Oceanic Physics
- 21 pages, 0 figures, minor modifications, version to appear in J. Phys. A. (2003)