Academic Journal
Relative energy constraint in Boltzmann's surface entropy eliminates thermodynamic inconsistencies and allows negative absolute temperatures
| العنوان: | Relative energy constraint in Boltzmann's surface entropy eliminates thermodynamic inconsistencies and allows negative absolute temperatures |
|---|---|
| المؤلفون: | Rajan, Ananth Govind |
| سنة النشر: | 2024 |
| المجموعة: | ArXiv.org (Cornell University Library) |
| مصطلحات موضوعية: | Condensed Matter - Statistical Mechanics |
| الوصف: | Over the past century, an intense debate in statistical mechanics has been about the correctness of Boltzmann's surface entropy versus Gibbs' volume entropy, for isolated systems. Both entropies make significantly different predictions for systems with few degrees of freedom. Even in the thermodynamic limit, they can disagree-while Boltzmann entropy allows negative absolute temperatures to exist, Gibbs entropy precludes such a possibility. Here, we show that modifying Boltzmann's entropy via a relative energy tolerance eliminates thermodynamic inconsistencies in several model systems with unbounded energy spectra by ensuring positive, finite temperatures. Concomitantly, the proposed entropy allows for negative temperatures in systems with bounded spectra and closely matches canonical ensemble predictions. This work conclusively remedies the prevalent deficiencies of the Gibbs and Boltzmann entropy formulations and paves the way for the use of the modified Boltzmann entropy in the microcanonical ensemble, allowing negative temperatures to exist. |
| نوع الوثيقة: | text |
| اللغة: | unknown |
| Relation: | http://arxiv.org/abs/2401.01838 |
| الاتاحة: | http://arxiv.org/abs/2401.01838 |
| رقم الانضمام: | edsbas.BF86BA6E |
| قاعدة البيانات: | BASE |
| ResultId |
1 |
|---|---|
| Header |
edsbas BASE edsbas.BF86BA6E 995 3 Academic Journal academicJournal 995.377258300781 |
| PLink |
https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&scope=site&db=edsbas&AN=edsbas.BF86BA6E&custid=s6537998&authtype=sso |
| FullText |
Array
(
[Availability] => 0
)
Array ( [0] => Array ( [Url] => http://arxiv.org/abs/2401.01838# [Name] => EDS - BASE [Category] => fullText [Text] => View record in BASE [MouseOverText] => View record in BASE ) ) |
| Items |
Array
(
[Name] => Title
[Label] => Title
[Group] => Ti
[Data] => Relative energy constraint in Boltzmann's surface entropy eliminates thermodynamic inconsistencies and allows negative absolute temperatures
)
Array ( [Name] => Author [Label] => Authors [Group] => Au [Data] => <searchLink fieldCode="AR" term="%22Rajan%2C+Ananth+Govind%22">Rajan, Ananth Govind</searchLink> ) Array ( [Name] => DatePubCY [Label] => Publication Year [Group] => Date [Data] => 2024 ) Array ( [Name] => Subset [Label] => Collection [Group] => HoldingsInfo [Data] => ArXiv.org (Cornell University Library) ) Array ( [Name] => Subject [Label] => Subject Terms [Group] => Su [Data] => <searchLink fieldCode="DE" term="%22Condensed+Matter+-+Statistical+Mechanics%22">Condensed Matter - Statistical Mechanics</searchLink> ) Array ( [Name] => Abstract [Label] => Description [Group] => Ab [Data] => Over the past century, an intense debate in statistical mechanics has been about the correctness of Boltzmann's surface entropy versus Gibbs' volume entropy, for isolated systems. Both entropies make significantly different predictions for systems with few degrees of freedom. Even in the thermodynamic limit, they can disagree-while Boltzmann entropy allows negative absolute temperatures to exist, Gibbs entropy precludes such a possibility. Here, we show that modifying Boltzmann's entropy via a relative energy tolerance eliminates thermodynamic inconsistencies in several model systems with unbounded energy spectra by ensuring positive, finite temperatures. Concomitantly, the proposed entropy allows for negative temperatures in systems with bounded spectra and closely matches canonical ensemble predictions. This work conclusively remedies the prevalent deficiencies of the Gibbs and Boltzmann entropy formulations and paves the way for the use of the modified Boltzmann entropy in the microcanonical ensemble, allowing negative temperatures to exist. ) Array ( [Name] => TypeDocument [Label] => Document Type [Group] => TypDoc [Data] => text ) Array ( [Name] => Language [Label] => Language [Group] => Lang [Data] => unknown ) Array ( [Name] => NoteTitleSource [Label] => Relation [Group] => SrcInfo [Data] => http://arxiv.org/abs/2401.01838 ) Array ( [Name] => URL [Label] => Availability [Group] => URL [Data] => http://arxiv.org/abs/2401.01838 ) Array ( [Name] => AN [Label] => Accession Number [Group] => ID [Data] => edsbas.BF86BA6E ) |
| RecordInfo |
Array
(
[BibEntity] => Array
(
[Languages] => Array
(
[0] => Array
(
[Text] => unknown
)
)
[Subjects] => Array
(
[0] => Array
(
[SubjectFull] => Condensed Matter - Statistical Mechanics
[Type] => general
)
)
[Titles] => Array
(
[0] => Array
(
[TitleFull] => Relative energy constraint in Boltzmann's surface entropy eliminates thermodynamic inconsistencies and allows negative absolute temperatures
[Type] => main
)
)
)
[BibRelationships] => Array
(
[HasContributorRelationships] => Array
(
[0] => Array
(
[PersonEntity] => Array
(
[Name] => Array
(
[NameFull] => Rajan, Ananth Govind
)
)
)
)
[IsPartOfRelationships] => Array
(
[0] => Array
(
[BibEntity] => Array
(
[Dates] => Array
(
[0] => Array
(
[D] => 01
[M] => 01
[Type] => published
[Y] => 2024
)
)
[Identifiers] => Array
(
[0] => Array
(
[Type] => issn-locals
[Value] => edsbas
)
[1] => Array
(
[Type] => issn-locals
[Value] => edsbas.oa
)
)
)
)
)
)
)
|
| IllustrationInfo |