Geometric Optimisation of Quantum Thermodynamic Processes

Area of Science:

• Thermodynamics
• Quantum Mechanics
• Differential Geometry
• Statistical Mechanics

Background:

• Finite-time thermodynamic processes are crucial for understanding real-world systems.
• Differential geometry offers a geometric perspective on thermodynamic state spaces.
• Existing frameworks for quantum thermodynamics lack a unified geometric approach.

Purpose of the Study:

• To introduce and explain the concept of thermodynamic length in classical and quantum regimes.
• To present a quantum generalization of the geometric lower bound on finite-time entropy production.
• To derive general principles for optimizing thermodynamic processes, particularly in the linear-response regime.

Main Methods:

• Pedagogical introduction to thermodynamic length.
• Review and connection of different quantum frameworks (adiabatic, Lindblad, discrete).
• Derivation of a geometric lower bound on entropy production.
• Analysis of optimization principles in the linear-response regime.

Main Results:

• Established thermodynamic length as a key concept in quantum thermodynamics.
• Presented a quantum geometric lower bound on entropy production.
• Identified optimal strategies for finite-time thermodynamic processes, including constant control speed and specific conditions for Carnot engines.

Conclusions:

• Differential geometry provides a powerful and unified framework for analyzing and optimizing thermodynamic processes.
• The introduced quantum entropy production bound offers new theoretical limits for thermodynamic efficiency.
• The derived optimization principles pave the way for designing more efficient classical and quantum engines and refrigerators.