Principles of maximum entropy and maximum caliber in statistical physics

Steve Pressé, Kingshuk Ghosh, Julian Lee, Ken A. Dill

Research output: Contribution to journalArticlepeer-review

269 Scopus citations


The variational principles called maximum entropy (MaxEnt) and maximum caliber (MaxCal) are reviewed. MaxEnt originated in the statistical physics of Boltzmann and Gibbs, as a theoretical tool for predicting the equilibrium states of thermal systems. Later, entropy maximization was also applied to matters of information, signal transmission, and image reconstruction. Recently, since the work of Shore and Johnson, MaxEnt has been regarded as a principle that is broader than either physics or information alone. MaxEnt is a procedure that ensures that inferences drawn from stochastic data satisfy basic self-consistency requirements. The different historical justifications for the entropy S=-Σipilogâ¡pi and its corresponding variational principles are reviewed. As an illustration of the broadening purview of maximum entropy principles, maximum caliber, which is path entropy maximization applied to the trajectories of dynamical systems, is also reviewed. Examples are given in which maximum caliber is used to interpret dynamical fluctuations in biology and on the nanoscale, in single-molecule and few-particle systems such as molecular motors, chemical reactions, biological feedback circuits, and diffusion in microfluidics devices.

Original languageEnglish (US)
Pages (from-to)1115-1141
Number of pages27
JournalReviews of Modern Physics
Issue number3
StatePublished - Jul 16 2013
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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