Trends in Gibbs States for Thermodynamics of Canonical Nonlinearity

TL;DR

This paper investigates the role of Gibbs states in the thermodynamics of canonical nonlinearity, revealing their concrete expressions, correlations with nonlinearity, and bounds within substitutional alloy systems.

Contribution

It provides a detailed analysis of Gibbs states' roles in canonical nonlinearity, including explicit expressions, correlations, and bounds, advancing understanding of nonlinear thermodynamic behavior.

Findings

Derived explicit expressions for Gibbs states.

Found strong correlation between Gibbs states and nonlinearity.

Established bounds for averaged nonlinearity based on Gibbs states.

Abstract

When we consider canonical average for classical discrete systems under constant composition (specifically, substitutional alloys) as a map phi from a set of many-body interatomic interactions to that of microscopic configuration in thermodynamic equilibrium, phi generally exhibits complicated nonlinearity. The nonlinearity has recently been amply studied in terms of configurational geometry, measured by vector field and Kullback-Leibler divergence, whose individual concepts are further unified through stochastic thermodynamic transformation: We call this procedure as Themodynamics of canonical nonlinearity (TCN). Although TCN can reveal the non-linear character across multiple configurations through thermodynamic functions, the essential role for Gibbs states (GBS) in terms of the nonlinearity is still totally unclear. We here tackle this problem, and reveal the characteristic roles of the GBS: (i) Concrete expression of the GBS is derived, (ii) strong correlation between GBSs and averaged nonlinearity over configurations for moled systems is found, and (iii) GBS-based bounds for averaged nonlinearity at specific conditions is derived.