Publication
[Not all characters may be displayed correctly. To be sure please proceed with the journal link.]
The Fermi-Pasta-Ulam (FPU) one-dimensional Hamiltonian includes a quartic term which guarantees ergodicity of the system in the thermodynamic limit. Consistently, the Boltzmann factor P(ϵ)∼e−βϵ describes its equilibrium distribution of one-body energies, and its velocity distribution is Maxwellian, i.e., P(v)∼e−βv2/2.
We consider here a generalized system where the quartic coupling constant between sites decays as 1/dαij (α≥0;dij=1,2,…). Through {it first-principle} molecular dynamics we demonstrate that, for large α (above α≃1), i.e., short-range interactions, Boltzmann statistics (based on the {it additive} entropic functional SB[P(z)]=−k∫dzP(z)lnP(z)) is verified. However, for small values of α (below α≃1), i.e., long-range interactions, Boltzmann statistics dramatically fails and is replaced by q-statistics (based on the {it nonadditive} entropic functional Sq[P(z)]=k(1−∫dz[P(z)]q)/(q−1), with S1=SB). Indeed, the one-body energy distribution is q-exponential, P(ϵ)∼e−βϵϵqϵ≡[1+(qϵ−1)βϵϵ]−1/(qϵ−1) with qϵ>1, and its velocity distribution is given by P(v)∼e−βvv2/2qv with qv>1. Moreover, within small error bars, we verify qϵ=qv=q, which decreases from an extrapolated value q ≃ 5/3 to q=1 when α increases from zero to α≃1, and remains q = 1 thereafter.
D. Bagchi, C. Tsallis, Fermi–Pasta–Ulam–Tsingou problems: Passage from Boltzmann to q-statistics, Physica A, Vol. 491 (2018) 869–873
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. |