Thermodynamic Approach for Nonlinearity within Canonical Ensemble

Abstract

In the field of classical discrete systems, specifically substitutional alloys, this study introduces a stochastic thermodynamic approach to address nonlinearity within a canonical ensemble. This approach establishes a nonlinear relationship between a spectrum of many-body interactions and the corresponding equilibrium configuration, as determined through the canonical average. The proposed method facilitates the analysis of nonlinearity across multiple configurations via newly introduced thermodynamic functions. These functions enable the formulation of nonlinearity in the configuration space, previously conceptualized as local, and extend it to nonlocal nonlinearity within statistical manifolds. The present findings indicate that the average nonlinearity disparity between partially ordered and other configurations is constrained by the entropy production in an ideal linear system. This system is comprehensively described by a covariance matrix of the density of states in the configuration space. Practically, this approach could significantly advance the analysis of nonlinearity for various classical discrete systems.