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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study dynamical reversibility in stationary stochastic processes from aninformation theoretic perspective. Extending earlier work on the reversibilityof Markov chains, we focus on finitary processes with arbitrarily longconditional correlations. In particular, we examine stationary processesrepresented or generated by edge-emitting, finite-state hidden Markov models.Surprisingly, we find pervasive temporal asymmetries in the statistics of suchstationary processes with the consequence that the computational resourcesnecessary to generate a process in the forward and reverse temporal directionsare generally not the same. In fact, an exhaustive survey indicates that moststationary processes are irreversible. We study the ensuing relations betweenmodel topology in different representations, the process's statisticalproperties, and its reversibility in detail. A process's temporal asymmetry isefficiently captured using two canonical unifilar representations of thegenerating model, the forward-time and reverse-time epsilon-machines. Weanalyze example irreversible processes whose epsilon-machine presentationschange size under time reversal, including one which has a finite number ofrecurrent causal states in one direction, but an infinite number in theopposite. From the forward-time and reverse-time epsilon-machines, we are ableto construct a symmetrized, but nonunifilar, generator of a process---thebidirectional machine. Using the bidirectional machine, we show how to directlycalculate a process's fundamental information properties, many of which areotherwise only poorly approximated via process samples. The tools we introduceand the insights we offer provide a better understanding of the many facets ofreversibility and irreversibility in stochastic processes.

Information Symmetries in Irreversible Processes