Formulation of Genuine Thermodynamic Variables from Special Microscopic States

TL;DR

This paper demonstrates that the Helmholtz free energy for disordered classical systems can be accurately estimated using a small set of specially selected microscopic states, bypassing the need for extensive thermodynamic data.

Contribution

It extends a theoretical framework to semi-grand canonical ensembles, enabling the determination of thermodynamic variables from limited microscopic state information.

Findings

Helmholtz free energy can be characterized by R+3 microscopic states.

The approach applies to disordered states at constant composition.

Temperature dependence of thermodynamic variables can be analyzed.

Abstract

For classical discrete systems under constant composition, it has been considered that genuine thermodynamic variables such as free energy cannot be generally determined from information about a single or a few selected microscopic states. Despite this fact, we here show that Helmholtz free energy for any given composition for disordered states can be well characterized by information about a few (R+3, where R denotes number of components) specially selected microscopic states, whose structure can be known a priori without requiring any thermodynamic information. The present study is a non-trivial extension of our recently-developed theoretical approach for special microscopic states in canonical ensemble to semi-grand canonical ensemble, which additionally enables to characterize temperature dependence of other thermodynamic variables such as internal energy and entropy.