Geometric structure and geodesic in a solvable model of nonequilibrium process

Area of Science:

• Statistical Mechanics
• Non-equilibrium Thermodynamics
• Geometric Methods

Background:

• Understanding the geometric structure of nonequilibrium processes is crucial for analyzing complex systems.
• Statistical metric spaces offer a framework to quantify information changes in dynamic systems.

Purpose of the Study:

• To investigate the geometric structure of nonequilibrium processes and identify geodesic solutions.
• To demonstrate the utility of geodesic paths for optimizing time and energy in driven dissipative systems.

Main Methods:

• Employed an exactly solvable model of a driven dissipative system (generalized nonautonomous Ornstein-Uhlenbeck process).
• Computed time-dependent probability density functions (PDFs).
• Investigated system evolution in a statistical metric space using information length.

Main Results:

• Identified a geodesic path in the statistical metric space where information propagates at a constant speed.
• Demonstrated that geodesic paths serve as optimal routes to reduce total time and dissipated energy.
• Observed a resonance phenomenon and discretization into cyclic geodesic solutions in physical realizations.

Conclusions:

• Geodesic solutions provide an optimal strategy for navigating complex nonequilibrium processes.
• The findings have implications for controlling population growth dynamics through stochastic models.