Central Approximation in Statistical Physics and Information Theory

TL;DR

This paper introduces a general framework combining the central approximation and the method of types to analyze detailed asymptotic behaviors of the partition function in statistical physics and information theory.

Contribution

It provides a novel approach for obtaining more precise asymptotic estimates of the partition function beyond the exponent.

Findings

Enhanced understanding of partition function asymptotics

Applicable to complex models in physics and information theory

Improves accuracy of theoretical predictions

Abstract

In statistical physics and information theory, although the exponent of the partition function is often of our primary interest, there are cases where one needs more detailed information. In this paper, we present a general framework to study more precise asymptotic behaviors of the partition function, using the central approximation in conjunction with the method of types.