Quantum counterpart of energy equipartition theorem for fermionic systems

TL;DR

This paper develops a quantum analogue of the energy equipartition theorem for fermionic systems, extending previous bosonic results to include multiple reservoirs and nonequilibrium steady states, with analysis of zero and low temperature effects.

Contribution

It introduces a general framework for the energy equipartition theorem in fermionic systems connected to multiple reservoirs, applicable far from equilibrium.

Findings

Mean energy expressed as an integral over reservoir frequencies.

Result valid for nonequilibrium steady states and nonlinear regimes.

Analysis of zero temperature and low temperature corrections.

Abstract

In this brief report, following the recent developments on formulating a quantum analogue of the classical energy equipartition theorem for open systems where the heat bath comprises of independent oscillators, i.e. bosonic degrees of freedom, we present an analogous result for fermionic systems. The most general case where the system is connected to multiple reservoirs is considered and the mean energy in the steady state is expressed as an integral over the reservoir frequencies. Physically this would correspond to summing over the contributions of the bath degrees of freedom to the mean energy of the system over a suitable distribution function $\rho(\omega)$ dependent on the system parameters. This result holds for nonequilibrium steady states, even in the nonlinear regime far from equilibrium. We also analyze the zero temperature behaviour and low temperature corrections to the mean energy of the system.