Fundamental limitations for quantum and nano thermodynamics

TL;DR

This paper develops a quantum thermodynamics framework for nano-scale systems, revealing fundamental limitations on work extraction and irreversibility due to quantum effects and finite size, impacting small heat engine efficiency.

Contribution

It introduces a quantum information-based theory of thermodynamics at small scales, deriving criteria for state transformations and identifying two distinct free energies.

Findings

Work extraction is limited by quantum coherences and finite size effects.

Thermodynamic transitions are generally irreversible at the nano scale.

Small heat engines exhibit irreversibility during adiabatic processes.

Abstract

The relationship between thermodynamics and statistical physics is valid in the thermodynamic limit - when the number of particles becomes very large. Here, we study thermodynamics in the opposite regime - at both the nano scale, and when quantum effects become important. Applying results from quantum information theory we construct a theory of thermodynamics in these limits. We derive general criteria for thermodynamical state transformations, and as special cases, find two free energies: one that quantifies the deterministically extractable work from a small system in contact with a heat bath, and the other that quantifies the reverse process. We find that there are fundamental limitations on work extraction from nonequilibrium states, owing to finite size effects and quantum coherences. This implies that thermodynamical transitions are generically irreversible at this scale. As one application of these methods, we analyse the efficiency of small heat engines and find that they are irreversible during the adiabatic stages of the cycle.