Interaction between Truth and Belief as the key to entropy and other quantities of statistical physics

Flemming Topsoe

Published 2008-07-27Version 1

The notion of entropy penetrates much of science. A key feature of the all-important notion of Boltzmann-Gibbs-Shannon entropy is its extensivity (additivity over independent subsystems). However, there is a need for other quantities. In statistical physics a parameterized family of non-extensive entropy measures, now mainly known under the name of Tsallis-entropies, have received much attention but also been met with criticism due mainly to a lack of convincing interpretations. Based on the hypothesis that interaction between Truth, held by ``Nature'', and Belief, as expressed by man, may take place, classical- as well as non-classical measures of entropy and other essential quantities are derived. The approach aims at providing a genuine interpretation, rather than relying either on analogies based on formal mathematical manipulations or else - more fruitfully, but not satisfactory - on axiomatic characterizations.