# Emergence of Tsallis statistics as a consequence of invariance

## TL;DR

This paper identifies two invariance-based conditions under which Tsallis statistics naturally arise in non-equilibrium steady states, providing a foundational understanding of their emergence.

## Contribution

It introduces invariance conditions that are both necessary and sufficient for the emergence of Tsallis statistics, independent of existing non-extensive frameworks.

## Key findings

- Tsallis statistics emerge under specific invariance conditions
- Conditions are necessary and sufficient for Tsallis ensemble formation
- Approach complements existing non-extensive and superstatistics theories

## Abstract

For non-equilibrium systems in a steady state we present two necessary and sufficient conditions for the emergence of $q$-canonical ensembles, also known as Tsallis statistics. These conditions are invariance requirements over the definition of subsystem and environment, and over the joint rescaling of temperature and energy. Our approach is independent of, but complementary to, the notions of Tsallis non-extensive statistics and Superstatistics.