Quantum Thermodynamics at Strong Coupling: Operator Thermodynamic Functions and Relations.

Area of Science:

• Physics
• Quantum Mechanics
• Thermodynamics

Background:

• Emergence in physical sciences, particularly thermodynamics, offers insights into complex systems.
• Traditional thermodynamics, based on large, weakly coupled systems, has limitations when applied to quantum phenomena.
• Understanding quantum mechanics as an emergent theory necessitates a robust framework for quantum thermodynamics.

Purpose of the Study:

• To establish the foundations of quantum thermodynamics for small quantum many-body systems.
• To address new issues and formulate rules for quantum systems strongly coupled to heat baths.
• To reexamine the meaning, viability, and validity of thermodynamic functions, relations, and laws in the quantum regime.

Main Methods:

• Overview of quantum formulations based on Gelin & Thoss and Seifert.
• Quantum formulation of Jarzynski's two representations.
• Construction of operator thermodynamic potentials and verification of their relations.

Main Results:

• Identified challenges in defining thermodynamic functions for quantum systems, especially at strong coupling.
• Demonstrated the construction of operator thermodynamic potentials yielding familiar thermodynamic variables.
• Highlighted subtleties in energy and entropy definitions and their operator forms in quantum thermodynamics.

Conclusions:

• Establishing a viable quantum thermodynamics requires constructing and verifying operator thermodynamic functions and their relations.
• Strong coupling in quantum systems introduces complexities not present in traditional thermodynamics.
• Further research is needed to develop a comprehensive theory of quantum thermodynamics.