Stochastic thermodynamics of quantum maps with and without equilibrium

Area of Science:

• Quantum thermodynamics
• Statistical mechanics
• Open quantum systems

Background:

• Stochastic thermodynamics analyzes fluctuations in small systems.
• Quantum systems interacting with baths are described by CPTP maps.
• Thermodynamic quantities often depend on system and environment states.

Purpose of the Study:

• To develop a quantum stochastic thermodynamics framework for CPTP maps.
• To simplify thermodynamic quantity calculations for systems in equilibrium.
• To derive fluctuation theorems for entropy production and work.

Main Methods:

• Definition of CPTP maps with equilibrium.
• Analysis of thermodynamic quantities in terms of system properties.
• Application of two-point measurement scheme for fluctuations.
• Derivation of entropy production fluctuation theorem and work fluctuation relation.

Main Results:

• Thermodynamic quantities expressed in system properties for maps with equilibrium.
• Valid for arbitrary system-bath coupling strengths.
• Entropy production and work fluctuation theorems derived.
• Simplifications for probability distributions in equilibrium cases.

Conclusions:

• The framework provides a unified approach to quantum stochastic thermodynamics.
• Equilibrium CPTP maps simplify thermodynamic calculations.
• The study connects CPTP maps to Lindblad equations and quantum detailed balance.