Generalized Einstein or Green-Kubo relations for active biomolecular transport

Area of Science:

• Biophysics
• Chemical Kinetics
• Statistical Mechanics

Background:

• Driven Markovian dynamics model complex systems.
• Generalized mobilities quantify system response to external parameters.
• Biomolecular systems often operate in nonequilibrium conditions.

Purpose of the Study:

• To establish a theoretical framework for generalized mobilities in driven Markovian dynamics.
• To relate generalized mobilities to current-current correlation functions.
• To demonstrate the applicability of this framework to nonequilibrium biomolecular systems.

Main Methods:

• Formulating generalized mobilities as integrals of current-current correlation functions.
• Utilizing the local detailed balance condition as the sole input requirement.
• Applying the theory to networks of biomolecular states.

Main Results:

• Generalized mobilities are directly expressed by integrals of current-current correlation functions.
• The derived relationship connects generalized mobilities to generalized diffusion constants.
• The framework is valid under the local detailed balance condition, common in biomolecular systems.

Conclusions:

• The study provides a theoretical link between generalized mobilities and correlation functions for driven Markovian dynamics.
• This approach is applicable to complex biomolecular systems operating far from equilibrium.
• The local detailed balance condition is a sufficient requirement for this theoretical framework.