Thermodynamic Potentials Theory Aspects in External Differential Forms Calculus Representation

Valerii V Shelest

doi:10.11648/j.jmpt.20170302.11

Abstract

Thorough review of external differential forms calculus basic theses presented. Potentialities of this mathematical discipline, which can describe physical properties of dielectric materials, magnets and photonic materials influenced by mechanical, thermal and electromagnetic factors more logically and objectively, then traditional methods, demonstrated. Methodological effectiveness of the differential forms of thermodynamic potentials application in the macroscopic properties of homogeneous mono- and polyvariant systems description has been demonstrated. The simple, fundamental, symmetrical to the thermodynamic variables choice relations demonstrating the calculus of differential forms benefits have been obtained. Using Pfaffian forms thermodynamics, have been demonstrated, that differential forms calculus application to a description of the physical reality allows to operate physical concepts at a deeper level, based on the fundamental physical and mathematical principles.

Highlights

The calculus of differential forms, which was created at the beginning of the XX century by E
In the opinion of many mathematicians [1,2,3,4], such traditional mathematical tools, as vector, differential and integral calculus, which are the foundation of usual theoretical physics mathematical apparatus, are to a certain extent not full constructive transfer of the more fundamental mathematical constructions external differential forms
The development of scientific thought has always sought to unify, simplicity and universality of physical concepts, which could be presented using the fundamental nature of the operator symbolism, and to operate with it

Summary

Introduction

The calculus of differential forms, which was created at the beginning of the XX century by E. On our opinion, using external differential forms calculus allows to expand thermodynamic language application field, to look to the standard relations from new point of view, consider ones on deeper scientific level. Shelest et al.: Thermodynamic Potentials Theory Aspects in External Differential Forms Calculus Representation laws consideration using direct differential calculus [5,6,7,8,9,10] and, at the same time, external differential forms calculus basic theses [1,2,3,4] Such an approach allows to look deeper to the thermodynamic laws in the view of abstract vector analysis and its geometrical images, which show physical reality nature from one more fundamental side, describing in mathematical physics by external multiplication and external differentiation concepts (see Appendix). Confirmation of initial principles is this article which demonstrated the simplicity of obtaining already known results and provided obtaining new ones conceptual scheme

Thermodynamic Potentials External Differential Forms Calculus

Remarks

Conclusions

Basic Theses

Concrete Applications

Formalism of Integration