The Legendre Transform in Non-Additive Thermodynamics and Complexity
<p dir="ltr">We present an argument which purports to show that the use of the standard Legendre transform in non-additive Statistical Mechanics is not appropriate. For concreteness, we use as paradigm, the case of systems which are conjecturally described by the (non-additive) Tsall...
محفوظ في:
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| منشور في: |
2017
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| _version_ | 1864513522154602496 |
|---|---|
| author | Nikolaos Kalogeropoulos (9416607) |
| author_facet | Nikolaos Kalogeropoulos (9416607) |
| author_role | author |
| dc.creator.none.fl_str_mv | Nikolaos Kalogeropoulos (9416607) |
| dc.date.none.fl_str_mv | 2017-06-01T00:00:00Z |
| dc.identifier.none.fl_str_mv | 10.3390/e19070298 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/The_Legendre_Transform_in_Non-Additive_Thermodynamics_and_Complexity/31446046 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Mathematical sciences Mathematical physics Physical sciences Classical physics Legendre transform statistical mechanics complex systems Tsallis entropy convexity |
| dc.title.none.fl_str_mv | The Legendre Transform in Non-Additive Thermodynamics and Complexity |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p dir="ltr">We present an argument which purports to show that the use of the standard Legendre transform in non-additive Statistical Mechanics is not appropriate. For concreteness, we use as paradigm, the case of systems which are conjecturally described by the (non-additive) Tsallis entropy. We point out the form of the modified Legendre transform that should be used, instead, in the non-additive thermodynamics induced by the Tsallis entropy. We comment on more general implications of this proposal for the thermodynamics of “complex systems”.</p><h2 dir="ltr">Other Information</h2><p dir="ltr">Published in: Entropy<br>License: <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank">https://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.3390/e19070298" target="_blank">https://dx.doi.org/10.3390/e19070298</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_727449e3e26b50eb1ef5bef6b25a326d |
| identifier_str_mv | 10.3390/e19070298 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/31446046 |
| publishDate | 2017 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | The Legendre Transform in Non-Additive Thermodynamics and ComplexityNikolaos Kalogeropoulos (9416607)Mathematical sciencesMathematical physicsPhysical sciencesClassical physicsLegendre transformstatistical mechanicscomplex systemsTsallis entropyconvexity<p dir="ltr">We present an argument which purports to show that the use of the standard Legendre transform in non-additive Statistical Mechanics is not appropriate. For concreteness, we use as paradigm, the case of systems which are conjecturally described by the (non-additive) Tsallis entropy. We point out the form of the modified Legendre transform that should be used, instead, in the non-additive thermodynamics induced by the Tsallis entropy. We comment on more general implications of this proposal for the thermodynamics of “complex systems”.</p><h2 dir="ltr">Other Information</h2><p dir="ltr">Published in: Entropy<br>License: <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank">https://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.3390/e19070298" target="_blank">https://dx.doi.org/10.3390/e19070298</a></p>2017-06-01T00:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.3390/e19070298https://figshare.com/articles/journal_contribution/The_Legendre_Transform_in_Non-Additive_Thermodynamics_and_Complexity/31446046CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/314460462017-06-01T00:00:00Z |
| spellingShingle | The Legendre Transform in Non-Additive Thermodynamics and Complexity Nikolaos Kalogeropoulos (9416607) Mathematical sciences Mathematical physics Physical sciences Classical physics Legendre transform statistical mechanics complex systems Tsallis entropy convexity |
| status_str | publishedVersion |
| title | The Legendre Transform in Non-Additive Thermodynamics and Complexity |
| title_full | The Legendre Transform in Non-Additive Thermodynamics and Complexity |
| title_fullStr | The Legendre Transform in Non-Additive Thermodynamics and Complexity |
| title_full_unstemmed | The Legendre Transform in Non-Additive Thermodynamics and Complexity |
| title_short | The Legendre Transform in Non-Additive Thermodynamics and Complexity |
| title_sort | The Legendre Transform in Non-Additive Thermodynamics and Complexity |
| topic | Mathematical sciences Mathematical physics Physical sciences Classical physics Legendre transform statistical mechanics complex systems Tsallis entropy convexity |