English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

There is a whole range of emergent phenomena in non-equilibrium behaviors canbe well described by a set of stochastic differential equations. Inspired by aninsight gained during our study of robustness and stability in phage lambdagenetic switch in modern biology, we found that there exists a classificationof generic nonequilibrium processes: In the continuous description in terms ofstochastic differential equations, there exists four dynamical elements: thepotential function $\phi$, the friction matrix $ S$, the anti-symmetric matrix$ T $, and the noise. The generic feature of absence of detailed balance isthen precisely represented by $T$. For dynamical near a fixed point, whether ornot it is stable or not, the stochastic dynamics is linear. A rather completeanalysis has been carried out (Kwon, Ao, Thouless, cond-mat/0506280; PNAS, {\bf102} (2005) 13029), referred to as SDS I. One important and persistent questionis the existence of a potential function with nonlinear force and withmultiplicative noise, with both nice local dynamical and global steady stateproperties. Here we demonstrate that a dynamical structure built intostochastic differential equation allows us to construct such a globaloptimization potential function. First, we provide the construction. One ofmost important ingredient is the generalized Einstein relation. We then presentan approximation scheme: The gradient expansion which turns every order intolinear matrix equations. The consistent of such methodology with other knownstochastic treatments will be discussed in next paper, SDS III; and theexplicitly connection to statistical mechanics and thermodynamics will bediscussed in a forthcoming paper, SDS IV.

journal of physics. a, mathematical and general/journal of physics. a, mathematical and general

Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the  Absence of Detailed Balance. II: construction of SDS with nonlinear force and  multiplicative noise