Geometric approach to nonequilibrium hasty shortcuts

Area of Science:

• Thermodynamics
• Non-equilibrium statistical mechanics
• Complex systems

Background:

• Thermodynamic systems can exhibit complex, non-monotonic responses to external control.
• Nonequilibrium processes offer pathways to rapidly transition systems between states.
• The Mpemba effect, where preheating enhances cooling, exemplifies counterintuitive nonequilibrium phenomena.

Purpose of the Study:

• To introduce and analyze nonequilibrium "hasty shortcuts" for rapid system steering.
• To develop a theoretical framework for understanding and identifying these shortcuts.
• To explore the diversity and characteristics of hasty shortcuts.

Main Methods:

• Geometric analysis in probability distribution space.
• Application of timescale separation and eigenmode decomposition.
• Numerical validation using a viral capsid self-assembly model.

Main Results:

• Identification of the necessary and sufficient conditions for hasty shortcuts.
• Classification of hasty shortcuts into categories based on temporal patterns.
• Demonstration that Mpemba-effect-like shortcuts are a subset of broader hasty shortcut categories.

Conclusions:

• Nonequilibrium hasty shortcuts provide a general method for rapid system control.
• The geometric approach reveals system features enabling these shortcuts.
• The theory is broadly applicable and numerically validated, offering insights into complex system dynamics.