Nonlinearity in Canonical Ensemble for Multicomponent Alloys Revisited from Structural Degree of Freedoms

Abstract

For a classical discrete system under constant composition, typically referred to as a substitutional alloys, we examine the local nonlinearity in the canonical average ϕ. We have investigated the local and global behavior of nonlinearity through the previously introduced vector field A and through the tropical limit of the vector field, respectively. While these studies indicated the importance of constraints to structural degrees of freedom (SDFs) for global nonlinearity, it is still unclear how the constraints to SDF affect the local nonlinearity. On the basis of a statistical manifold, we make an intuitive bridge between the SDF-based information and the local nonlinearity, decomposing the local nonlinearity into two (for binary alloys with pair correlations) or three (for otherwise) contributions in terms of the Kullback–Leibler divergence, where this decomposition is independent of temperature and many-body interaction, and is defined on individual configurations. We also find that we can provide A-dependent as well as A-independent decompositions of the local nonlinearity, where nonseparability in SDFs and its nonadditive character are independent of A, which indicates that information about the evolution of the vector field should be required to address the nonseparability and nonadditivity. The present work enables to quantify how configuration-dependent constraints to SDF affect local nonlinearity in the canonical average for multicomponent alloys.