Generalized information and entropy measures in physics

Abstract

The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of information measures that are useful for the description of complex systems. Examples treated are the Renyi entropy, Tsallis entropy, Abe entropy, Kaniadakis entropy, Sharma-Mittal entropies, and a few more. Important concepts such as the axiomatic foundations, composability and Lesche stability of information measures are briefly discussed. Potential applications in physics include complex systems with long-range interactions and metastable states, scattering processes in particle physics, hydrodynamic turbulence, defect turbulence, optical lattices, and quite generally driven nonequilibrium systems with fluctuations of temperature.

23 pages, 6 figures. Short review article, to appear in Contemporary Physics. References extended

References in corpus (7)

• Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
• Superstatistics, thermodynamics, and fluctuations
• Defect turbulence and generalized statistical mechanics
• Statistics of 3-dimensional Lagrangian turbulence
• Superstatistical distributions from a maximum entropy principle
• A two-parameter generalization of Shannon-Khinchin Axioms and the uniqueness theorem
• On the robustness of q-expectation values and Renyi entropy

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