Groups, information theory, and Einstein's likelihood principle
Abstract
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a grouptheoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the ShannonKhinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.
 Publication:

Physical Review E
 Pub Date:
 April 2016
 DOI:
 10.1103/PhysRevE.93.040101
 arXiv:
 arXiv:1512.00089
 Bibcode:
 2016PhRvE..93d0101S
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 5 pages