Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields
Time reversal invariance (TRI) of particles systems has many consequences, among which the celebrated Onsager reciprocal relations, a milestone in Statistical Mechanics dating back to 1931. Because for a long time it was believed that (TRI) dos not hold in presence of a magnetic field, a modificatio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/8/1336 |
| _version_ | 1797559173359075328 |
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| author | Davide Carbone Lamberto Rondoni |
| author_facet | Davide Carbone Lamberto Rondoni |
| author_sort | Davide Carbone |
| collection | DOAJ |
| description | Time reversal invariance (TRI) of particles systems has many consequences, among which the celebrated Onsager reciprocal relations, a milestone in Statistical Mechanics dating back to 1931. Because for a long time it was believed that (TRI) dos not hold in presence of a magnetic field, a modification of such relations was proposed by Casimir in 1945. Only in the last decade, the strict traditional notion of reversibility that led to Casimir’s work has been questioned. It was then found that other symmetries can be used, which allow the Onsager reciprocal relations to hold without modification. In this paper we advance this investigation for classical Hamiltonian systems, substantially increasing the number of symmetries that yield TRI in presence of a magnetic field. We first deduce the most general form of a generalized time reversal operation on the phase space of such a system; secondly, we express sufficient conditions on the magnetic field which ensure TRI. Finally, we examine common examples from statistical mechanics and molecular dynamics. Our main result is that TRI holds in a much wider generality than previously believed, partially explaining why no experimental violation of Onsager relations has so far been reported. |
| first_indexed | 2024-03-10T17:41:39Z |
| format | Article |
| id | doaj.art-4b84804195a7433285ec141368bcbff4 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T17:41:39Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-4b84804195a7433285ec141368bcbff42023-11-20T09:40:41ZengMDPI AGSymmetry2073-89942020-08-01128133610.3390/sym12081336Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic FieldsDavide Carbone0Lamberto Rondoni1Dipartimento di Fisica, Università di Torino, Via Pietro Giuria 1, 10125 Torino, ItalyDipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, ItalyTime reversal invariance (TRI) of particles systems has many consequences, among which the celebrated Onsager reciprocal relations, a milestone in Statistical Mechanics dating back to 1931. Because for a long time it was believed that (TRI) dos not hold in presence of a magnetic field, a modification of such relations was proposed by Casimir in 1945. Only in the last decade, the strict traditional notion of reversibility that led to Casimir’s work has been questioned. It was then found that other symmetries can be used, which allow the Onsager reciprocal relations to hold without modification. In this paper we advance this investigation for classical Hamiltonian systems, substantially increasing the number of symmetries that yield TRI in presence of a magnetic field. We first deduce the most general form of a generalized time reversal operation on the phase space of such a system; secondly, we express sufficient conditions on the magnetic field which ensure TRI. Finally, we examine common examples from statistical mechanics and molecular dynamics. Our main result is that TRI holds in a much wider generality than previously believed, partially explaining why no experimental violation of Onsager relations has so far been reported.https://www.mdpi.com/2073-8994/12/8/1336hamiltonian dynamicsmagnetic fieldcorrelation functionsonsager reciprocal relations |
| spellingShingle | Davide Carbone Lamberto Rondoni Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields Symmetry hamiltonian dynamics magnetic field correlation functions onsager reciprocal relations |
| title | Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields |
| title_full | Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields |
| title_fullStr | Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields |
| title_full_unstemmed | Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields |
| title_short | Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields |
| title_sort | necessary and sufficient conditions for time reversal symmetry in presence of magnetic fields |
| topic | hamiltonian dynamics magnetic field correlation functions onsager reciprocal relations |
| url | https://www.mdpi.com/2073-8994/12/8/1336 |
| work_keys_str_mv | AT davidecarbone necessaryandsufficientconditionsfortimereversalsymmetryinpresenceofmagneticfields AT lambertorondoni necessaryandsufficientconditionsfortimereversalsymmetryinpresenceofmagneticfields |