Geometrical Field Formulation of Thermomechanics in Rational Mechanics

TL;DR

This paper proposes a geometrical field approach to thermomechanics, integrating quantum motion and configuration deformation to unify atomic physics and engineering mechanics.

Contribution

It introduces a novel formulation combining quantum state wave functions and deformation geometry to describe thermomechanical behavior.

Findings

Couples quantum and configuration motions in thermomechanics

Reinterprets entropy within a geometrical and quantum framework

Recovers classical elasticity and statistical physics limits

Abstract

In modern science, the thermo mechanics motion can be traced back to quantum motion in micro viewpoint. On the other hand, the thermo mechanics is definitely related with geometrical configuration motion (phase) in macro viewpoint. On this sense, the thermomechanics should be formulated by two kinds of motion: quantum motion and configuration motion. Its principle goal ought to be bridge the gap between atomic physics and engineering practice. In this research, the configuration motion is formulated by deformation geometrical field (motion transformation tensor). The quantum motion is formulated by the wave function of quantum state. Based on these two fields, the thermo stress is formulated as the coupling of quantum motion and configuration motion. Along this line, the entropy is interpreted and formulated according to thermodynamics rules. For scalar entropy, the traditional meaning of entropy is reserved. For infinitesimal configuration variation, the formulation is degenerated to the traditional elasticity deformation. For large random configuration deformation, the formulation is degenerated to the statistical physics methods. This research supplies a possible formulation to bridge the gap between the macro deformation and the micro quantum motion.