Publication
Complex systems with strong correlations and fat-tailed distribution functions have been argued to be incompatible with the Boltzmann-Gibbs entropy framework and alternatives, so-called generalised entropies, were proposed and studied.
Here we show, that this perceived incompatibility is actually a misconception. For a broad class of processes, Boltzmann entropy –the log multiplicity– remains the valid entropy concept. However, for non-i.i.d. processes, Boltzmann entropy is not of Shannon form, −k∑ipi log pi, but takes the shape of generalised entropies.
We derive this result for all processes that can be asymptotically mapped to adjoint representations reversibly where processes are i.i.d. In these representations the information production is given by the Shannon entropy. Over the original sampling space this yields functionals identical to generalised entropies.
The problem of constructing adequate context-sensitive entropy functionals therefore can be translated into the much simpler problem of finding adjoint representations. The method provides a comprehensive framework for a statistical physics of strongly correlated systems and complex processes.
R. Hanel, S. Thurner, Equivalence of information production and generalised entropies in complex processes, PLOS ONE 18(9) (2023) e0290695.
Related
Signup
Cookie | Duration | Description |
---|---|---|
cookielawinfo-checkbox-analytics | 1 year | Set by the GDPR Cookie Consent plugin, this cookie records the user consent for the cookies in the "Analytics" category. |
cookielawinfo-checkbox-functional | 1 year | The GDPR Cookie Consent plugin sets the cookie to record the user consent for the cookies in the category "Functional". |
cookielawinfo-checkbox-necessary | 1 year | Set by the GDPR Cookie Consent plugin, this cookie records the user consent for the cookies in the "Necessary" category. |
CookieLawInfoConsent | 1 year | CookieYes sets this cookie to record the default button state of the corresponding category and the status of CCPA. It works only in coordination with the primary cookie. |
PHPSESSID | session | This cookie is native to PHP applications. The cookie stores and identifies a user's unique session ID to manage user sessions on the website. The cookie is a session cookie and will be deleted when all the browser windows are closed. |
viewed_cookie_policy | 1 year | The GDPR Cookie Consent plugin sets the cookie to store whether or not the user has consented to use cookies. It does not store any personal data. |
Cookie | Duration | Description |
---|---|---|
mec_cart | 1 month | Provides functionality for our ticket shop |
VISITOR_INFO1_LIVE | 6 months | YouTube sets this cookie to measure bandwidth, determining whether the user gets the new or old player interface. |
VISITOR_PRIVACY_METADATA | 6 months | YouTube sets this cookie to store the user's cookie consent state for the current domain. |
YSC | session | Youtube sets this cookie to track the views of embedded videos on Youtube pages. |
yt-remote-connected-devices | never | YouTube sets this cookie to store the user's video preferences using embedded YouTube videos. |
yt-remote-device-id | never | YouTube sets this cookie to store the user's video preferences using embedded YouTube videos. |
yt.innertube::nextId | never | YouTube sets this cookie to register a unique ID to store data on what videos from YouTube the user has seen. |
yt.innertube::requests | never | YouTube sets this cookie to register a unique ID to store data on what videos from YouTube the user has seen. |
Cookie | Duration | Description |
---|---|---|
_ga | 1 year | Google Analytics sets this cookie to calculate visitor, session and campaign data and track site usage for the site's analytics report. The cookie stores information anonymously and assigns a randomly generated number to recognise unique visitors. |
_ga_* | 1 year | Google Analytics sets this cookie to store and count page views. |
_gat_gtag_UA_* | 1 min | Google Analytics sets this cookie to store a unique user ID. |
_gid | 1 day | Google Analytics sets this cookie to store information on how visitors use a website while also creating an analytics report of the website's performance. Some of the collected data includes the number of visitors, their source, and the pages they visit anonymously. |