Geodesic path for the optimal nonequilibrium transition: Momentum-independent protocol

Area of Science:

• Thermodynamics
• Quantum Control
• Statistical Mechanics

Background:

• Accelerating controlled thermodynamic processes necessitates auxiliary Hamiltonians for rapid equilibrium.
• Finite-time operations incur unavoidable extra energy costs.
• Previous geodesic approaches minimized energy for isothermal processes but required complex momentum-dependent controls.

Purpose of the Study:

• To develop a variational auxiliary control that approximates exact control without momentum-dependent terms.
• To minimize energy cost for finite-time thermodynamic processes using a geometric approach.
• To demonstrate the practical implementation of this protocol for Brownian motion.

Main Methods:

• Employed a variational auxiliary control strategy, omitting momentum-dependent forces.
• Utilized a geometric approach to derive the optimal control protocol.
• Applied the method to a Brownian motion system with a controllable harmonic potential.

Main Results:

• Obtained an optimal control protocol with a variational minimum energy cost.
• The proposed control method simplifies experimental implementation by removing speed-monitoring requirements.
• Successfully demonstrated the protocol's construction using a Brownian motion example.

Conclusions:

• The variational auxiliary control offers a practical and energy-efficient method for accelerating thermodynamic processes.
• This approach significantly reduces experimental complexity compared to previous methods.
• The findings pave the way for more feasible experimental realizations of fast thermodynamic control.