Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 110, Issue 37, Pages 14930-14935Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1305604110
Keywords
nonequilibrium landscape; adiabaticity; nonadiabaticity
Categories
Funding
- National Science Foundation of China [21190040, 11174105]
- 973 Project [2009CB930100, 2010CB933600]
- Japan Society for the Promotion of Science [24244068, 23654147]
- National Science Foundation
- Grants-in-Aid for Scientific Research [23654147] Funding Source: KAKEN
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Physical and biological systems are often involved with coupled processes of different time scales. In the system with electronic and atomic motions, for example, the interplay between the atomic motion along the same energy landscape and the electronic hopping between different landscapes is critical: the system behavior largely depends on whether the intralandscape motion is slower (adiabatic) or faster (nonadiabatic) than the interlandscape hopping. For general nonequilibrium dynamics where Hamiltonian or energy function is unknown a priori, the challenge is how to extend the concepts of the intra-and interlandscape dynamics. In this paper we establish a theoretical framework for describing global nonequilibrium and nonadiabatic complex system dynamics by transforming the coupled landscapes into a single landscape but with additional dimensions. On this single landscape, dynamics is driven by gradient of the potential landscape, which is closely related to the steady-state probability distribution of the enlarged dimensions, and the probability flux, which has a curl nature. Through an example of a self-regulating gene circuit, we show that the curl flux has dramatic effects on gene regulatory dynamics. The curl flux and landscape framework developed here are easy to visualize and can be used to guide further investigation of physical and biological nonequilibrium systems.
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