Thermodynamics of Extended Bodies in Special Relativity

TL;DR

This paper extends relativistic thermodynamics to include four-dimensional rotations, deriving the thermodynamics of bodies undergoing spatial rotation and linear acceleration, beyond the traditionally studied translational motion.

Contribution

It generalizes relativistic thermodynamics to encompass four-dimensional rotations, providing new thermodynamic descriptions for rotating and accelerating bodies in flat spacetime.

Findings

Derived thermodynamics for bodies in spatial rotation.

Derived thermodynamics for bodies under constant linear acceleration.

Extended the understanding of equilibrium conditions in relativistic settings.

Abstract

Relativistic thermodynamics is generalized to accommodate four dimensional rotation in a flat spacetime. An extended body can be in equilibrium when its each element moves along a Killing flow. There are three types of basic Killing flows in a flat spacetime, each of which corresponds to translational motion, spatial rotation, and constant linear acceleration; spatial rotation and constant linear acceleration are regarded as four dimensional rotation. Translational motion has been mainly investigated in the past literature of relativistic thermodynamics. Thermodynamics of the other two is derived in the present paper.