Mathematical expressions for quantum fluctuations of energy for different energy-momentum tensors

TL;DR

This paper derives formulas for quantum energy fluctuations in hot relativistic gases, emphasizing the dependence on the energy-momentum tensor's pseudo-gauge choice, highlighting their importance in small thermodynamic systems.

Contribution

It provides new expressions for quantum energy fluctuations that depend on the pseudo-gauge choice of the energy-momentum tensor in relativistic gases.

Findings

Quantum fluctuations depend on the pseudo-gauge choice.

Fluctuations are significant in small thermodynamic systems.

Results highlight the importance of considering quantum effects in microscopic systems.

Abstract

Expressions for the quantum fluctuations of energy density have been derived for the subsystems consisting of hot relativistic gas of particles with spin-$\frac{1}{2}$ and mass $m$. Our expressions for the fluctuation depend on the form of energy-momentum tensor which in turn depend on the choice of pseudo-gauge. These results suggest that quantum fluctuations of energy should be considered seriously in the case of the very small thermodynamic systems.