TITLE:
The Method of Thermomechanical Dynamics (TMD) and the Application to the Concept of Maxwell’s Demon
AUTHORS:
Hiroshi Uechi, Lisa Uechi, Schun Toma Uechi
KEYWORDS:
Thermomechanical Dynamics (TMD), Maxwell’s Demon, Measure for Nonequilibrium Irreversible States, Homeostatic Equilibrium, Thermodynamic Time and Mechanical Clock Time
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.5,
May
18,
2026
ABSTRACT: The method of thermomechanical dynamics (TMD) has successfully explained mechanisms of heat engines and heat-energy flows, time-dependent physical quantities and the phase transition from thermodynamic equilibrium to nonequilibrium irreversible states (NISs). In the current paper, the TMD is applied to study the physical meaning and mathematical expression of Maxwell’s demon. The analysis results in the extension of the traditional, disordered, static thermodynamic equilibrium to accommodate stable, structured and closed nonequilibrium thermodynamic systems. The new image of thermodynamic equilibrium is termed as the homeostatic equilibrium, which shall be an appropriate foundation for nonequilibrium irreversible dynamics of the thermal, macroscopic world. The interrelated fundamental problems, such as the concept of time and causality, the thermodynamic time and the mechanical clock time are discussed in detail by the method of TMD.