Relativistic mechanical-thermodynamical formalism -- description of inelastic collisions

TL;DR

This paper introduces a relativistic formalism based on Minkowski four-vectors that incorporates thermodynamic conservation laws, specifically applied to inelastic collisions, bridging classical and relativistic mechanics.

Contribution

It develops a new relativistic formalism that combines four-vector mechanics with thermodynamics, specifically addressing inelastic collisions.

Findings

Formalism successfully describes inelastic collisions relativistically.

Connects classical and relativistic conservation laws.

Provides a framework for analyzing thermodynamic processes in relativistic contexts.

Abstract

We present a relativistic formalism inspired on the Minkowski four-vectors that also includes conservation laws such as the first law of thermodynamics. It remains close to the relativistic four-vector formalism developed for a single particle, but it is also related to the classical treatment of problems that imperatively require both the Newton's second law and the energy conservation law. We apply the developed formalism to inelastic collisions to better show how it works.