Analytical results and universal behavior in fast thermal equilibration protocols.

Area of Science:

• Statistical Mechanics and Thermodynamics
• Non-equilibrium Systems
• Quantum Control

Background:

• Systems deviating from equilibrium can be controlled to reach equilibrium in finite time.
• Shortcut-to-equilibrium protocols manipulate systems, often reducing relaxation timescales.
• Analytical solutions for work, heat, and entropy distributions in these protocols are scarce.

Purpose of the Study:

• To propose a generalizable two-step protocol for shortcut-to-equilibrium processes.
• To derive analytical solutions for thermodynamic probability distributions (work, heat, entropy).
• To investigate universal behaviors in the limit of very short protocol durations.

Main Methods:

• Development of a simplified two-step control protocol.
• Analytical derivation of probability distributions for thermodynamic quantities.
• Analysis of system behavior for protocol durations much shorter than relaxation time (t_f ≪ τ_relax).

Main Results:

• The proposed two-step protocol yields analytical solutions for work, heat, and entropy distributions.
• Evidence of universal behavior is found for the ratio of probability distributions of positive and negative work, heat, and produced entropy.
• This universality emerges in the regime of very short protocol durations (t_f ≪ τ_relax).

Conclusions:

• The study provides a tractable model for analyzing shortcut-to-equilibrium protocols.
• Analytical results for thermodynamic quantities are achievable, offering deeper insights.
• Universal scaling laws govern short-time dynamics, simplifying the understanding of non-equilibrium processes.