Generalized information and entropy measures in physics

TL;DR

This paper explores generalized information measures like Renyi, Tsallis, and others, extending statistical mechanics to better describe complex physical systems with non-standard interactions and states.

Contribution

It reviews various generalized entropy measures, discussing their axiomatic foundations, stability, and potential applications in complex and nonequilibrium physical systems.

Findings

Highlights the importance of non-Shannon entropies in physics

Discusses stability and composability of generalized measures

Suggests applications in turbulence, particle physics, and driven systems

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.