A general maximum entropy framework for thermodynamic variational principles
- Research School of Biology, The Australian National University, Canberra ACT 0200 (Australia)
Minimum free energy principles are familiar in equilibrium thermodynamics, as expressions of the second law. They also appear in statistical mechanics as variational approximation schemes, such as the mean-field and steepest-descent approximations. These well-known minimum free energy principles are here unified and extended to any system analyzable by MaxEnt, including non-equilibrium systems. The MaxEnt Lagrangian associated with a generic MaxEnt distribution p defines a generalized potential Ψ for an arbitrary probability distribution p-hat, such that Ψ is a minimum at (p-hat) = p. Minimization of Ψ with respect to p-hat thus constitutes a generic variational principle, and is equivalent to minimizing the Kullback-Leibler divergence between p-hat and p. Illustrative examples of min–Ψ are given for equilibrium and non-equilibrium systems. An interpretation of changes in Ψ is given in terms of the second law, although min–Ψ itself is an intrinsic variational property of MaxEnt that is distinct from the second law.
- OSTI ID:
- 22390756
- Journal Information:
- AIP Conference Proceedings, Vol. 1636, Issue 1; Conference: MaxEnt 2013: 33. International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Canberra, ACT (Australia), 15-20 Dec 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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