A compact formula for the quantum fluctuations of energy

TL;DR

This paper derives a formula to compute quantum energy fluctuations in small subsystems of hot, relativistic gases, revealing size-dependent behavior and aligning with canonical ensemble predictions at larger scales, with applications in high-energy physics.

Contribution

The paper introduces a new compact formula for quantum energy fluctuations applicable to relativistic gases, bridging microscopic quantum effects with macroscopic thermodynamic concepts.

Findings

Fluctuations increase in smaller subsystems.

The formula agrees with canonical ensemble results for large sizes.

Applicable to high-temperature, high-velocity matter in various physics fields.

Abstract

A formula to calculate the quantum fluctuations of energy in small subsystems of a hot and relativistic gas is derived. We find an increase in fluctuations for subsystems of small sizes, but we agrees with the energy fluctuations in the canonical ensemble if the size is large enough. Not only one can use our expression to find the limit of the concepts of energy density or fluid element in connection to relativistic heavy-ion collisions, but also in other areas of physics where one studies matter with high temperature and velocity.