Trajectory Entropy of Continuous Stochastic Processes at Equilibrium.
We propose to quantify the trajectory entropy of a dynamic system as the information content in excess of a free-diffusion reference model. The space-time trajectory is now the dynamic variable, and its path probability is given by the Onsager-Machlup action. For the time propagation of the overdamped Langevin equation, we solved the action path integral in the continuum limit and arrived at an exact analytical expression that emerged as a simple functional of the deterministic mean force and the stochastic diffusion. This work may have direct implications in chemical and phase equilibria, bond isomerization, and conformational changes in biological macromolecules as well transport problems in general.
†Department of Chemical and Biomolecular Engineering, University of California-Berkeley, 201 Gilman Hall, Berkeley, California 94720, United States.
Kevin R
KR
Haas
‡Department of Chemistry, Princeton University, Washington Road, Princeton, New Jersey 08544, United States.
Haw
H
Yang
§Department of Biological Science and Technology, National Chiao Tung University, 75 Bo-Ai Street, Hsinchu, Taiwan, ROC.|∥Institute of Bioinformatics and Systems Biology, National Chiao Tung University, Hsinchu, Taiwan, ROC.
Jhih-Wei
JW
Chu
overdamped Langevin dynamics; trajectory entropy; trajectory path integral