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Trajectory Entropy of Continuous Stochastic Processes at Equilibrium.
Kevin R Haas1, Haw Yang2, Jhih-Wei Chu3,4
1†Department of Chemical and Biomolecular Engineering, University of California-Berkeley, 201 Gilman Hall, Berkeley, California 94720, United States.
The Journal of Physical Chemistry Letters
|August 14, 2015
Summary
We introduce trajectory entropy to measure information in dynamic systems beyond free diffusion. This new metric, derived from the Onsager-Machlup action, offers insights into complex molecular and transport processes.
Area of Science:
- Statistical Mechanics
- Physical Chemistry
- Biophysics
Background:
- Dynamic systems analysis often relies on simplified models.
- Quantifying information content in complex trajectories is challenging.
- Existing methods may not fully capture system dynamics.
Purpose of the Study:
- To develop a novel method for quantifying trajectory entropy.
- To establish a theoretical framework for information content in dynamic systems.
- To provide a more accurate measure of system dynamics beyond free diffusion.
Main Methods:
- Formulating trajectory entropy based on information excess over free diffusion.
- Utilizing the Onsager-Machlup action for path probability in space-time.
- Solving the action path integral for the overdamped Langevin equation in the continuum limit.
Main Results:
- An exact analytical expression for trajectory entropy was derived.
- The expression is a simple functional of mean force and diffusion.
- This provides a quantifiable measure of information in system trajectories.
Conclusions:
- The proposed trajectory entropy offers a powerful tool for analyzing dynamic systems.
- This framework has broad applicability in chemical, biological, and transport phenomena.
- It enhances our understanding of molecular conformational changes and phase equilibria.
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