Clausius inequality for finite baths reveals universal efficiency improvements

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Quantum Physics

Background:

• Nanoscale devices are increasingly coupled to finite heat baths, a scenario with growing experimental relevance.
• Existing theoretical approaches often rely on the second law formulation for infinite baths, which is inadequate for these systems.
• This necessitates a revised understanding of thermodynamic laws in finite-bath systems.

Purpose of the Study:

• To address the limitations of current theoretical frameworks for entropy production in nanoscale devices coupled to finite heat baths.
• To re-evaluate and apply Clausius's 1865 formulation of the second law for finite heat baths.
• To extend fundamental principles like Landauer's principle to finite bath conditions and analyze their impact on heat engine efficiency.

Main Methods:

• Revisiting and applying Clausius's 1865 inequality for finite heat baths.
• Rigorous derivation of the Clausius inequality from a microscopic quantum description.
• Extension of Landauer's principle to systems interacting with finite heat baths.
• Analysis of heat engine efficiency under finite bath conditions.

Main Results:

• Clausius's inequality offers an adequate formulation of the second law for finite heat baths.
• Nonequilibrium processes in finite baths are less irreversible than previously considered.
• Landauer's principle is correctly extended to finite baths.
• Heat engines coupled to finite baths exhibit higher efficiency than predicted by traditional models.

Conclusions:

• The study provides a robust theoretical framework for understanding entropy production in nanoscale devices with finite heat baths.
• The findings suggest that thermodynamic irreversibility is lower and heat engine efficiency is higher in finite bath systems than commonly assumed.
• The results are experimentally accessible, requiring only knowledge of the average bath energy.