Random activation energy model and disordered kinetics, from static to dynamic disorder.

Area of Science:

• Statistical Mechanics
• Chemical Kinetics
• Disordered Systems

Background:

• Random rate processes with energy barriers are common in various scientific fields.
• Understanding the impact of static and dynamic disorder is crucial for accurate kinetic modeling.
• Existing models often struggle to encompass the full spectrum of disorder types.

Purpose of the Study:

• To develop a unified path integral approach for random rate processes with random energy barriers.
• To provide a framework that includes static and dynamic disorder as special cases.
• To enable exact computation of the average survival function for disordered kinetics.

Main Methods:

• Utilizing a generalized Zubarev-McLennan nonequilibrium statistical ensemble.
• Deriving the ensemble from the maximum information entropy approach.
• Employing path integral formalism for calculating the characteristic functional.

Main Results:

• The average survival function is exactly computable via the characteristic functional of the generalized ensemble.
• Expressions for the average survival function are derived for diverse disorder types (static, long/short memory, no memory).
• A model of dynamic disorder of the renewal type is analyzed as an illustration.

Conclusions:

• The unified approach effectively models various disorder types in random rate processes.
• The derived expressions facilitate precise evaluation of kinetic parameters from experimental data.
• The framework has potential implications for molecular biology and genetics.