Kinetic Theory with Casimir Invariants—Toward Understanding of Self-Organization by Topological Constraints
A topological constraint, characterized by the Casimir invariant, imparts non-trivial structures in a complex system. We construct a kinetic theory in a constrained phase space (infinite-dimensional function space of macroscopic fields), and characterize a self-organized structure as a thermal equil...
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MDPI AG
2024-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/27/1/5 |
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| author | Zensho Yoshida |
| author_facet | Zensho Yoshida |
| author_sort | Zensho Yoshida |
| collection | DOAJ |
| description | A topological constraint, characterized by the Casimir invariant, imparts non-trivial structures in a complex system. We construct a kinetic theory in a constrained phase space (infinite-dimensional function space of macroscopic fields), and characterize a self-organized structure as a thermal equilibrium on a leaf of foliated phase space. By introducing a model of a grand canonical ensemble, the Casimir invariant is interpreted as the number of topological particles. |
| format | Article |
| id | doaj-art-7669652f2e204699abe62cd5b98ecf7c |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-7669652f2e204699abe62cd5b98ecf7c2025-01-24T13:31:37ZengMDPI AGEntropy1099-43002024-12-01271510.3390/e27010005Kinetic Theory with Casimir Invariants—Toward Understanding of Self-Organization by Topological ConstraintsZensho Yoshida0National Institute for Fusion Science, Oroshi, Toki 509-5292, Gifu, JapanA topological constraint, characterized by the Casimir invariant, imparts non-trivial structures in a complex system. We construct a kinetic theory in a constrained phase space (infinite-dimensional function space of macroscopic fields), and characterize a self-organized structure as a thermal equilibrium on a leaf of foliated phase space. By introducing a model of a grand canonical ensemble, the Casimir invariant is interpreted as the number of topological particles.https://www.mdpi.com/1099-4300/27/1/5self-organizationtopological constraintCasimir invariantnoncanonical Hamiltonian systemco-adjoint representation |
| spellingShingle | Zensho Yoshida Kinetic Theory with Casimir Invariants—Toward Understanding of Self-Organization by Topological Constraints Entropy self-organization topological constraint Casimir invariant noncanonical Hamiltonian system co-adjoint representation |
| title | Kinetic Theory with Casimir Invariants—Toward Understanding of Self-Organization by Topological Constraints |
| title_full | Kinetic Theory with Casimir Invariants—Toward Understanding of Self-Organization by Topological Constraints |
| title_fullStr | Kinetic Theory with Casimir Invariants—Toward Understanding of Self-Organization by Topological Constraints |
| title_full_unstemmed | Kinetic Theory with Casimir Invariants—Toward Understanding of Self-Organization by Topological Constraints |
| title_short | Kinetic Theory with Casimir Invariants—Toward Understanding of Self-Organization by Topological Constraints |
| title_sort | kinetic theory with casimir invariants toward understanding of self organization by topological constraints |
| topic | self-organization topological constraint Casimir invariant noncanonical Hamiltonian system co-adjoint representation |
| url | https://www.mdpi.com/1099-4300/27/1/5 |
| work_keys_str_mv | AT zenshoyoshida kinetictheorywithcasimirinvariantstowardunderstandingofselforganizationbytopologicalconstraints |