Effective temperature for finite systems

TL;DR

This paper introduces a method to determine an effective temperature for finite systems based on occupation times, applicable without a known Hamiltonian, demonstrated with a Bose gas and network traffic analysis.

Contribution

It presents a novel approach to compute effective temperature directly from occupation data, independent of the system's Hamiltonian, for finite systems.

Findings

Effective temperature can be uniquely determined from occupation times.

Method applied successfully to classical Bose gas.

Analysis of computer network traffic using the proposed approach.

Abstract

Under the Ansatz that the occupation times of a system with finitely many states are given by the Gibbs distribution, an effective temperature is uniquely determined (up to a choice of scale), and may be computed de novo, without any reference to a Hamiltonian for empirically accessible systems. As an example, the calculation of the effective temperature for a classical Bose gas is outlined and applied to the analysis of computer network traffic.