Generalised information and entropy measures in physics

• Published in: Contemporary physics Vol. 50; no. 4; pp. 495 - 510
• Main Author: Beck, Christian
• Format: Journal Article
• Language: English
• Published: Colchester Taylor & Francis 01.07.2009; Taylor & Francis Ltd
• Subjects: Classical statistical mechanics; Complex systems; Entropy; Exact sciences and technology; generalised statistical mechanics; Information; measures of information; Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Information measure; Turbulence; Long range interaction; Non equilibrium system; Metastable states; Complex system; Entropy; Statistical mechanics; Renyi theory; Temperature fluctuation
• ISSN: 0010-7514; 1366-5812
• DOI: 10.1080/00107510902823517

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.