Physical meaning and a duality of concepts of wave function, action functional, entropy, the Pointing vector, the Einstein tensor

TL;DR

This paper explores the dual nature of fundamental physical concepts like wave function and entropy, revealing their roles as both functionals and state functions through the use of skew-symmetric forms.

Contribution

It introduces a duality framework for physical concepts using skew-symmetric forms, linking their functional and state-based roles in mathematical physics.

Findings

Duality of concepts revealed through skew-symmetric forms

Transition from functionals to state functions explains physical structure origin

Application to entropy and action demonstrates the framework's utility

Abstract

Physical meaning and a duality of concepts of wave function, action functional, entropy, the Pointing vector, the Einstein tensor and so on can be disclosed by investigating the state of material systems such as thermodynamic and gas dynamic systems, systems of charged particles, cosmologic systems and others. These concepts play a same role in mathematical physics. They are quantities that specify a state of material systems and also characteristics of physical fields. The duality of these concepts reveals in the fact that they can at once be both functionals and state functions or potentials. As functionals they are defined on nonintegrable manifold (for example, on tangent one), and as a state function they are defined on integrable manifold (for example, on cotangent one). The transition from functionals to state functions dicribes the mechanism of physical structure origination. The properties of these concepts can be studied by the example of entropy and action. The role of these concepts in mathematical physics and field theory will be demonstrated. Such results have been obtained by using skew-symmetric forms. In addition to exterior forms, the skew-symmetric forms, which are obtained from differential equations and, in distinction to exterior forms, are evolutionary ones and are defined on nonintegrable manifolds, were used.