PIRSA:21020045

Change the coefficients of conditional entropies in extensivity

APA

Takatsu, A. (2021). Change the coefficients of conditional entropies in extensivity. Perimeter Institute. https://pirsa.org/21020045

MLA

Takatsu, Asuka. Change the coefficients of conditional entropies in extensivity. Perimeter Institute, Feb. 25, 2021, https://pirsa.org/21020045

BibTex

          @misc{ pirsa_21020045,
            doi = {10.48660/21020045},
            url = {https://pirsa.org/21020045},
            author = {Takatsu, Asuka},
            keywords = {Mathematical physics},
            language = {en},
            title = {Change the coefficients of conditional entropies in extensivity},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {feb},
            note = {PIRSA:21020045 see, \url{https://pirsa.org}}
          }
          

Asuka Takatsu Tokyo Metropolitan University

Abstract

The Boltzmann--Gibbs entropy is a functional on the space of probability measures. One characterization of the Boltzmann--Gibbs entropy is given by the Shannon--Khinchin axioms, which consist of continuity, maximality, expandability and extensivity. The extensivity is expressed in terms of the linear combinations of conditional probabilities. Replacing the coefficients in the linear combinations with a power function provides a characterization of the Tsallis entropy. I talk about the impossibility to replace the coefficients with a non-power function.