Information theory explanation of the fluctuation theorem, maximum entropy production and selforganized criticality in nonequilibrium stationary states
Abstract
Jaynes' information theory formalism of statistical mechanics is applied to the stationary states of open, nonequilibrium systems. First, it is shown that the probability distribution p_{Gamma} of the underlying microscopic phase space trajectories Gamma over a time interval of length tau satisfies p_{Gamma} propto exp(tausigma_{Gamma}/2k_{B}) where sigma_{Gamma} is the timeaveraged 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 nonequilibrium 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 selforganized criticality for fluxdriven systems in the slowlydriven limit. The explanation of these results on general information theoretic grounds underlines their relevance to a broad class of stationary, nonequilibrium systems. In turn, the accumulating empirical evidence for these results lends support to Jaynes' formalism as a common predictive framework for equilibrium and nonequilibrium statistical mechanics.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 January 2003
 DOI:
 10.1088/03054470/36/3/303
 arXiv:
 arXiv:condmat/0005382
 Bibcode:
 2003JPhA...36..631D
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Physics  Atmospheric and Oceanic Physics
 EPrint:
 21 pages, 0 figures, minor modifications, version to appear in J. Phys. A. (2003)