Deformed exponentials and logarithms in generalized thermostatistics

TL;DR

This paper introduces criteria for kappa-deformed logarithmic and exponential functions and demonstrates how they can be used to formulate generalized thermostatistics.

Contribution

It establishes a framework for using kappa-deformed functions and their deduced logarithms in generalized thermostatistics.

Findings

Criteria for kappa-deformed functions are provided.

Generalized thermostatistics can be formulated with these functions.

The relationship between deformed exponentials and logarithms is clarified.

Abstract

Criteria are given that kappa-deformed logarithmic and exponential functions should satisfy. With a pair of such functions one can associate another function, called the deduced logarithmic function. It is shown that generalized thermostatistics can be formulated in terms of kappa-deformed exponential functions together with the associated deduced logarithmic functions.