# On superstatistics of energy for a free quantum Brownian particle

## TL;DR

This paper explores the energy distribution and thermodynamics of a quantum Brownian particle using superstatistics, highlighting the effects of coupling strength and memory effects on energy and specific heat.

## Contribution

It introduces a quantum analogue of the energy equipartition theorem derived from fluctuation-dissipation relations, incorporating superstatistics to analyze quantum energetics.

## Key findings

- Energy and specific heat depend on coupling strength.
- Memory effects influence energy fluctuations.
- Quantum superstatistics provides new insights into quantum thermodynamics.

## Abstract

We consider energetics of a free quantum Brownian particle coupled to thermostat of temperature $T$ and study this problem in terms of the lately formulated quantum analogue of the energy equipartition theorem. We show how this quantum counterpart can be derived from the Callen-Welton fluctuation-dissipation relation and rephrased in terms of superstatistics. We analyse the influence of the system-thermostat coupling strength and the memory time of the dissipation kernel on statistical characteristics of the particle energy and its specific heat.