Geometry of Work Fluctuations versus Efficiency in Microscopic Thermal Machines

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Quantum Information

Background:

• Engineering microscopic machines often faces a trade-off between efficiency and reliability due to stochastic fluctuations.
• Optimizing these systems requires balancing competing objectives, particularly in the classical and quantum regimes.

Purpose of the Study:

• To develop a general method for multiobjective optimization of efficiency and work fluctuations in thermal machines.
• To apply techniques from thermodynamic geometry to characterize optimal protocols.

Main Methods:

• Utilizing thermodynamic geometry to match optimal solutions to protocols.
• Parametrizing protocols by their thermodynamic length.
• Analyzing continuous-variable Gaussian machines.

Main Results:

• A general method for optimizing efficiency and work fluctuations in thermal machines was developed.
• Optimal protocols were characterized for continuous-variable Gaussian machines.
• The approach is applicable to both classical and quantum thermal machines operating near equilibrium.

Conclusions:

• The developed method provides a framework for designing more reliable and efficient microscopic thermal machines.
• Thermodynamic geometry offers powerful tools for understanding and optimizing complex thermodynamic systems.
• This research advances the field of thermodynamics for microscopic systems.