Dynamical Equations For The Period Vectors In A Periodic System Under Constant External Stress

TL;DR

This paper derives dynamical equations for the period vectors of a periodic system under constant external stress, highlighting the role of internal and external stress imbalance in driving system evolution.

Contribution

It introduces a novel derivation of period vector dynamics based on Newton's laws and stress analysis, incorporating both interaction and kinetic energy contributions.

Findings

Dynamical equations relate period vectors to stress imbalance.

Internal stress includes interaction and kinetic energy terms.

External stress influences the evolution of the system's periodic structure.

Abstract

The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton's second law applied to halves of the system. Later statistics over indistinguishable translated states and forces associated with transport of momentum are applied to the resulting dynamical equations. In the final expressions, the period vectors are driven by the imbalance between internal and external stresses. The internal stress is shown to have both full interaction and kinetic-energy terms.