On Higher Order Structures in Thermodynamics
We present the development of the approach to thermodynamics based on measurement. First of all, we recall that considering classical thermodynamics as a theory of measurement of extensive variables one gets the description of thermodynamic states as Legendrian or Lagrangian manifolds representing t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/10/1147 |
| _version_ | 1797551240400338944 |
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| author | Valentin Lychagin Mikhail Roop |
| author_facet | Valentin Lychagin Mikhail Roop |
| author_sort | Valentin Lychagin |
| collection | DOAJ |
| description | We present the development of the approach to thermodynamics based on measurement. First of all, we recall that considering classical thermodynamics as a theory of measurement of extensive variables one gets the description of thermodynamic states as Legendrian or Lagrangian manifolds representing the average of measurable quantities and extremal measures. Secondly, the variance of random vectors induces the Riemannian structures on the corresponding manifolds. Computing higher order central moments, one drives to the corresponding higher order structures, namely the cubic and the fourth order forms. The cubic form is responsible for the skewness of the extremal distribution. The condition for it to be zero gives us so-called symmetric processes. The positivity of the fourth order structure gives us an additional requirement to thermodynamic state. |
| first_indexed | 2024-03-10T15:41:46Z |
| format | Article |
| id | doaj.art-bf535edcf4034eadb0b4b3e554434fa1 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T15:41:46Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-bf535edcf4034eadb0b4b3e554434fa12023-11-20T16:47:48ZengMDPI AGEntropy1099-43002020-10-012210114710.3390/e22101147On Higher Order Structures in ThermodynamicsValentin Lychagin0Mikhail Roop1V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Str., 117997 Moscow, RussiaV.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Str., 117997 Moscow, RussiaWe present the development of the approach to thermodynamics based on measurement. First of all, we recall that considering classical thermodynamics as a theory of measurement of extensive variables one gets the description of thermodynamic states as Legendrian or Lagrangian manifolds representing the average of measurable quantities and extremal measures. Secondly, the variance of random vectors induces the Riemannian structures on the corresponding manifolds. Computing higher order central moments, one drives to the corresponding higher order structures, namely the cubic and the fourth order forms. The cubic form is responsible for the skewness of the extremal distribution. The condition for it to be zero gives us so-called symmetric processes. The positivity of the fourth order structure gives us an additional requirement to thermodynamic state.https://www.mdpi.com/1099-4300/22/10/1147thermodynamic statesLegendrian and Lagrangian manifoldsvarianceskewness |
| spellingShingle | Valentin Lychagin Mikhail Roop On Higher Order Structures in Thermodynamics Entropy thermodynamic states Legendrian and Lagrangian manifolds variance skewness |
| title | On Higher Order Structures in Thermodynamics |
| title_full | On Higher Order Structures in Thermodynamics |
| title_fullStr | On Higher Order Structures in Thermodynamics |
| title_full_unstemmed | On Higher Order Structures in Thermodynamics |
| title_short | On Higher Order Structures in Thermodynamics |
| title_sort | on higher order structures in thermodynamics |
| topic | thermodynamic states Legendrian and Lagrangian manifolds variance skewness |
| url | https://www.mdpi.com/1099-4300/22/10/1147 |
| work_keys_str_mv | AT valentinlychagin onhigherorderstructuresinthermodynamics AT mikhailroop onhigherorderstructuresinthermodynamics |