Generalised information and entropy measures in physics

By Christian Beck. 2009

257 citations recorded by the source corpus.

The formalism of statistical mechanics can be generalised by starting from more general measures of information than the Shannon entropy and maximising 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 Rényi 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.

Subfields: Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/40381180022145b0dc0aa1fedf5884cf9d6c34b3

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Citations in the corpus

Some Characterization Results on Dynamic Cumulative Residual Tsallis Entropy (2015, background): “However, Renyi entropy is an extensive entropy which is the major difference between them (cf. [19, 20]).”
Rationally Inattentive Behavior: Characterizing and Generalizing Shannon Entropy (2017, background): “To understand the behavioral implications of uniform posterior separability, note that so long as the support of μ remains unchanged, μ enters additively in (7) and changes in μ do not affect the relative cost of any posterior.”