# Non-extensive thermodynamics of 1D systems with long-range interaction

## TL;DR

This paper introduces a new framework for non-extensive thermodynamics applied to 1D systems with long-range interactions, using Markov chains to derive asymptotic energy and entropy expressions.

## Contribution

It proposes a novel approach linking non-extensive thermodynamics with additive Markov chains, specifically applied to long-range interacting Ising chains.

## Key findings

- Energy and entropy are non-proportional to system size in the weak interaction limit.
- Derived asymptotic expressions for thermodynamic quantities.
- Established a connection between non-extensive thermodynamics and Markov chain models.

## Abstract

A new approach to non-extensive thermodynamical systems with non-additive energy and entropy is proposed. The main idea of the paper is based on the statistical matching of the thermodynamical systems with the additive multi-step Markov chains. This general approach is applied to the Ising spin chain with long-range interaction between its elements. The asymptotical expressions for the energy and entropy of the system are derived for the limiting case of weak interaction. These thermodynamical quantities are found to be non-proportional to the length of the system (number of its particle).