Year: 2007
Type: conference-paper
Abstract: Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann) we demonstrate how the corresponding entropy has to look like, given the form of the corresponding distribution functions. By two natural assumptions that (i) the maximum entropy principle should hold and that (ii) entropy should describe the correct thermodynamics of a system (which produces non-Boltzmann distributions) the existence of a class of fully consistent entropies can be deduced. Classical Boltzmann-Gibbs entropy is recovered as a special case for the observed distribution being the exponential, Tsallis entropy is the special case for q-exponential observations.
Source: AIP conference proceedings
DOI: 10.1063/1.2828761
Authors: Stefan Thurner, Rudolf Hanel, Sumiyoshi Abe, Hans Herrmann, Piero Quarati, Andrea Rapisarda, Constantino Tsallis
Institutions: Santa Fe Institute, Medical University of Vienna
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1502290952