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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Many systems in nature and laboratories are far from equilibrium and exhibitsignificant fluctuations, invalidating the key assumptions of smallfluctuations and short memory time in or near equilibrium. A full knowledge ofProbability Distribution Functions (PDFs), especially time-dependent PDFs,becomes essential in understanding far-from-equilibrium processes. We considera stochastic logistic model with multiplicative noise, which has gammadistributions as stationary PDFs. We numerically solve the transient relaxationproblem, and show that as the strength of the stochastic noise increases thetime-dependent PDFs increasingly deviate from gamma distributions. Forsufficiently strong noise a transition occurs whereby the PDF never reaches astationary state, but instead forms a peak that becomes ever more narrowlyconcentrated at the origin. The addition of an arbitrarily small amount ofadditive noise regularizes these solutions, and re-establishes the existence ofstationary solutions. In addition to diagnostic quantities such as mean value,standard deviation, skewness and kurtosis, the transitions between differentsolutions are analyzed in terms of entropy and information length, the totalnumber of statistically distinguishable states that a system passes through intime.

Far-from-Equilibrium Time Evolution between two Gamma Distributions