Conservation laws. Their role in evolutionary processes (The method of skew-symmetric differential forms)

TL;DR

This paper explores two types of conservation laws—exact and balance—and their roles in physical structures and material systems, using skew-symmetric differential forms to reveal their interrelation in evolutionary processes.

Contribution

It introduces a mathematical framework using skew-symmetric differential forms to relate exact and balance conservation laws in physical and material systems.

Findings

Exact conservation laws relate to physical structures.

Balance laws govern material system dynamics.

Noncommutativity of balance laws drives physical structure formation.

Abstract

In the work it has been shown that there are two types of the conservation laws. 1. The conservation laws that can be called exact ones. They point to an avalability of some conservative quantities or objects. Such objects are the physical structures, which the physical fields and relevant manifolds are constructed of. These are conservation laws for physical fields. 2. The conservation laws of energy, linear and angular momentum, and mass. These laws are conservation laws for material systems (material media). They establish a balance between changes of physical quantities and external actions. Such conservation laws can be called as balance ones. It has been shown that the exact and balance conservation laws execute a relation between the physical structures, which form physical fields, and material systems. The physical structures, to which the exact conservation laws correspond, are generated by material systems in the evolutionary processes, whose moving force is the noncommutativity of the balance conservation laws. These results are obtained with the help of the mathematical apparatus of skew-symmetric differential forms.