Quantum statistical fluctuation of energy and its novel pseudo-gauge dependence

TL;DR

This paper investigates quantum statistical energy fluctuations in relativistic gases, revealing size-dependent effects and pseudo-gauge dependence for spin-half particles, with implications for small-system thermal physics.

Contribution

It introduces a detailed analysis of quantum energy fluctuations in relativistic gases, highlighting pseudo-gauge dependence and system size effects, extending understanding of quantum fluctuations in thermal systems.

Findings

Quantum fluctuations increase as system size decreases.

For spin-half particles, fluctuations depend on pseudo-gauge choices.

Large systems show convergence to canonical ensemble results.

Abstract

We discuss the quantum statistical fluctuations of energy in subsystems of hot relativistic gas for both spin-zero and spin half particles. We explicitly show the system size dependence of the quantum statistical fluctuation of energy. Our results show that with decreasing system size quantum statistical fluctuations increase substantially. As the consistency of the framework, we also argue that the quantum statistical fluctuations give rise to the known result for statistical fluctuation of energy in the canonical ensemble if we consider the size of the subsystem to be sufficiently large. For a spin-half particle quantum fluctuations show some interesting novel features. We show that within a small sub-system quantum statistical fluctuation of energy for spin half particles depends on the various pseudo-gauge choices of the energy-momentum tensor. Interestingly, for sufficiently large subsystems quantum fluctuations obtained for different pseudo-gauge choices converge and we recover the canonical-ensemble formula known for statistical fluctuations of energy. Our calculation is very general and can be applied to any branch of physics whenever one deals with a thermal system. As a practical application, we argue that our results can be used to determine a coarse-graining scale to introduce the concept of classical energy density or fluid element relevant for the strongly interacting matter, in particular for small systems produced in heavy-ion collisions.