Quantum statistics and the performance of engine cycles

TL;DR

This paper investigates how quantum statistics influence the efficiency of Otto engine cycles, revealing that bosonic and fermionic work distributions are identical in harmonic traps but differ in non-harmonic potentials due to energy level spacing effects.

Contribution

It analytically compares bosonic and fermionic work distributions in quantum Otto cycles and explores how different trapping potentials affect engine performance.

Findings

Work distributions are identical for bosons and fermions in harmonic traps.

Energy level spacing significantly impacts engine performance in non-harmonic potentials.

Different potential shapes lead to varied effects of quantum statistics on cycle efficiency.

Abstract

We study the role of quantum statistics in the performance of Otto cycles. First, we show analytically that the work distributions for bosonic and fermionic working fluids are identical for cycles driven by harmonic trapping potentials. Subsequently, in the case of non-harmonic potentials, we find that the interplay between different energy level spacings and particle statistics strongly affects the performances of the engine cycle. To demonstrate this, we examine three trapping potentials which induce different (single particle) energy level spacings: monotonically decreasing with the level number, monotonically increasing, and the case in which the level spacing does not vary monotonically.