Optimal Selection of Structural Degree of Freedoms for Spceial Microscopic States to Characterize Disordered Structures

TL;DR

This paper proposes a systematic criterion for selecting the optimal set of structural degrees of freedom to construct projection states that characterize disordered structures without requiring thermodynamic information.

Contribution

It introduces a quantitative method for choosing the most relevant structural degrees of freedom for disordered states, enhancing the construction of projection states.

Findings

Effective criteria for constructing projection states

Guidelines for selecting structural degrees of freedom

Insights into the influence of SDFs on equilibrium properties

Abstract

For classical discrete systems under constant composition, statistical mechanics tells us that a set of microscopic state dominantly contributing to thermodynamically equilibrium state should depend on temperature as well as on many-body interaction (i.e. thermodynamic information), through Boltzamann factor of exp(-bE). Despite this fact, our recent study reveals that a single (and a few additional) microscopic state (called projection state: PS), whose structure can be known a priori without r equiring thermodynamic information, can universally characterize equiibrium properties for disordered states, where their sturctures depends on configurational geometry before applying many-body interaction to the system. Although mathematical condition for the structures of PS have been rigorously established, practically effective condition for constructing the stuructures, especially for which set of a finite structural degree of freedoms (SDF) should be selected for considered coordination has not been clarified so far. We here tuckle this problem, proposing a quantitative and systematic criteria for an optimal set of SDFs. The present proposal enables to effectively constructing PSs for a limited system size, and also providing new insight into which set of SDFs should generally affects equilibrium properties along a chosen coordination, without using any thermodynamic information.