Nonadditive thermostatistics and thermodynamics

TL;DR

This paper explores nonadditive thermodynamic rules, linking formal logarithms and Tsallis entropy, and connects the parameter q to generalized susceptibilities of thermostats.

Contribution

It introduces a framework where nonadditive composition rules are derived from thermodynamic principles, establishing a connection between formal logarithms, the zeroth law, and Tsallis entropy.

Findings

Formal logarithms are derived from the zeroth law.

The parameter q in Tsallis entropy relates to generalized susceptibilities.

Universal thermostat independence constrains the form of nonadditive rules.

Abstract

Nonadditive composition rules for several physical quantities are treated in thermodynamics. It is argued that the zeroth law defines the existence of their additive forms, the formal logarithms. A further principle, the universal thermostat independence leads to a particular formal logarithm, equivalent to Tsallis entropy S_q. We connect q with generalized susceptibilities of the thermostat.