Journal
REVIEWS OF MODERN PHYSICS
Volume 85, Issue 3, Pages 1115-1141Publisher
AMER PHYSICAL SOC
DOI: 10.1103/RevModPhys.85.1115
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Funding
- NIH [R01GM090205-03]
- IUPUI
- Research Corporation for Science Advancement
- Direct For Mathematical & Physical Scien
- Division Of Physics [1205881] Funding Source: National Science Foundation
- Div Of Molecular and Cellular Bioscience
- Direct For Biological Sciences [1051344] Funding Source: National Science Foundation
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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 = -Sigma(i)p(i) log p(i) 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.
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