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

We review the behaviour of the Gibbs' and conditional entropies indeterministic and stochastic systems with the added twist of a formulationappropriate for a stochastically perturbed system with {\it delayed} dynamics.The underlying question driving these investigations: ``Is the origin of theuniversally observed unidirectionality of time in our universe connected to thebehaviour of entropy?"  We focus on temporal entropic behaviour with a review of previous results indeterministic and stochastic systems. Our emphasis is on the temporal behaviourof the Gibbs' and conditional entropies as they give equilibrium results inconcordance with experimental findings. In invertible deterministic systemsboth entropies are temporally constant as has been well known for decades. Theaddition of stochastic perturbations (Wiener process) leads to an indeterminate(either increasing or decreasing) behaviour of the Gibbs' entropy, but theconditional entropy monotonically approaches equilibrium with increasing time.The presence of delays in the dynamics, whether stochastically perturbed ornot, leads to situations in which the Gibbs' and conditional entropiesevolution can be oscillatory and not monotone, and may not approachequilibrium.

Temporal Entropy Evolution in Stochastic and Delayed Dynamics