Special Microscopic-states-basis Formulation of Macroscopic Structure for Thermodynamic Systems

TL;DR

This paper introduces a new microscopic states basis approach to determine macroscopic structures in thermodynamic systems, extending previous high-temperature methods to lower temperatures above transition points.

Contribution

It develops a framework to identify special microscopic states that characterize equilibrium structures across a broader temperature range, beyond high-temperature regimes.

Findings

Universal microscopic state at high temperature (projection state) identified.

Extended approach to lower temperatures above transition temperature.

Framework enables macroscopic property formulation via special microscopic states.

Abstract

For classical system under constant composition, macroscopic structure in thermodynamically equilibrium state can be determined through the so-called canonical average, including sum over possible microscopic states on phase space. Although a set of microscopic structure dominantly contributing to equilibrium properties should depend on temperature and many-body interactions, we recently clarify that at high temperature, they are universally characterized by a single special microscopic state (which we call projection state: PS), whose structure can be known a priori without any thermodynamic information. Here we extend this approach to find additional special microscopic states, enabling us to characterize equilibrium structures for lower-temperature region above transition temperature. The concept of our approach will lead to a new paradigm; the formulation of macroscopic properties by special microscopic states basis.