Undeformed (additive) energy conservation law in Doubly Special Relativity

TL;DR

This paper demonstrates the existence of Doubly Special Relativity models that maintain additive energy conservation, enabling consistent DSR thermodynamics and covariant energy definitions.

Contribution

It introduces DSR models that preserve additive energy conservation, contrasting with previous models that deformed energy rules.

Findings

Existence of DSR models with additive energy conservation

Construction of DSR-covariant extensive energy

Implications for multiparticle system dynamics

Abstract

All the Doubly Special Relativity (DSR) models studied in literature so far involve a deformation of the energy conservation rule that forces us to release the hypothesis of the additivity of the energy for composite systems. In view of the importance of the issue for a consistent formulation of a DSR statistical mechanics and a DSR thermodynamics, we show that DSR models preserving the usual (i.e. additive) energy conservation rule can be found. These models allow the construction of a DSR-covariant extensive energy. The implications of the analysis for the dynamics of DSR-covariant multiparticle systems are also briefly discussed.