Thermodynamics of nonadditive systems

TL;DR

This paper develops a thermodynamic framework for nonadditive systems with long-range interactions by using an ensemble of replicas, enabling the application of standard thermodynamics to such systems.

Contribution

It introduces a novel approach to describe nonadditive systems within thermodynamics using replicas, extending the formalism to long-range interacting systems.

Findings

Applicable to systems with interactions decaying as 1/r^α with α<d

Successfully applied to the Thirring model for gravitational systems

Provides a unified thermodynamic description for nonadditive systems

Abstract

The usual formulation of thermodynamics is based on the additivity of macroscopic systems. However, there are numerous examples of macroscopic systems that are not additive, due to the long-range character of the interaction among the constituents. We present here an approach in which nonadditive systems can be described within a purely thermodynamics formalism. The basic concept is to consider a large ensemble of replicas of the system where the standard formulation of thermodynamics can be naturally applied and the properties of a single system can be consequently inferred. After presenting the approach, we show its implementation in systems where the interaction decays as $1/r^\alpha$ in the interparticle distance $r$, with $\alpha$ smaller than the embedding dimension $d$, and in the Thirring model for gravitational systems.