A Monte Carlo Method for Calculating Lynden-Bell Equilibrium in Self-Gravitating Systems
We present a Monte Carlo approach that allows us to easily implement Lynden-Bell (LB) entropy maximization for an arbitrary initial particle distribution. The direct maximization of LB entropy for an arbitrary initial distribution requires an infinite number of Lagrange multipliers to account for th...
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| Format: | Article |
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MDPI AG
2023-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/10/1379 |
| _version_ | 1827721073762762752 |
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| author | Tarcísio N. Teles Calvin A. F. Farias Renato Pakter Yan Levin |
| author_facet | Tarcísio N. Teles Calvin A. F. Farias Renato Pakter Yan Levin |
| author_sort | Tarcísio N. Teles |
| collection | DOAJ |
| description | We present a Monte Carlo approach that allows us to easily implement Lynden-Bell (LB) entropy maximization for an arbitrary initial particle distribution. The direct maximization of LB entropy for an arbitrary initial distribution requires an infinite number of Lagrange multipliers to account for the Casimir invariants. This has restricted studies of Lynden-Bell’s violent relaxation theory to only a very small class of initial conditions of a very simple waterbag form, for which the entropy maximization can be performed numerically. In the present approach, an arbitrary initial distribution is discretized into density levels which are then evolved using an efficient Monte Carlo algorithm towards the final equilibrium state. A comparison is also made between the LB equilibrium and explicit Molecular Dynamics simulations. We find that for most initial distributions, relaxation is incomplete and the system is not able to reach the state of maximum LB entropy. In particular, we see that the tail of the stationary particle distribution is very different from the one predicted by the theory of violent relaxation, with a hard cutoff instead of an algebraic decay predicted by LB’s theory. |
| first_indexed | 2024-03-10T21:16:46Z |
| format | Article |
| id | doaj.art-92e74f83d22245e4b49a99973a05d01f |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T21:16:46Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-92e74f83d22245e4b49a99973a05d01f2023-11-19T16:24:04ZengMDPI AGEntropy1099-43002023-09-012510137910.3390/e25101379A Monte Carlo Method for Calculating Lynden-Bell Equilibrium in Self-Gravitating SystemsTarcísio N. Teles0Calvin A. F. Farias1Renato Pakter2Yan Levin3Grupo de Física de Feixes, Universidade Federal de Ciências da Saúde de Porto Alegre (UFCSPA), Porto Alegre 90050-170, RS, BrazilInstituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Caixa Postal 15051, Porto Alegre 91501-970, RS, BrazilInstituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Caixa Postal 15051, Porto Alegre 91501-970, RS, BrazilInstituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Caixa Postal 15051, Porto Alegre 91501-970, RS, BrazilWe present a Monte Carlo approach that allows us to easily implement Lynden-Bell (LB) entropy maximization for an arbitrary initial particle distribution. The direct maximization of LB entropy for an arbitrary initial distribution requires an infinite number of Lagrange multipliers to account for the Casimir invariants. This has restricted studies of Lynden-Bell’s violent relaxation theory to only a very small class of initial conditions of a very simple waterbag form, for which the entropy maximization can be performed numerically. In the present approach, an arbitrary initial distribution is discretized into density levels which are then evolved using an efficient Monte Carlo algorithm towards the final equilibrium state. A comparison is also made between the LB equilibrium and explicit Molecular Dynamics simulations. We find that for most initial distributions, relaxation is incomplete and the system is not able to reach the state of maximum LB entropy. In particular, we see that the tail of the stationary particle distribution is very different from the one predicted by the theory of violent relaxation, with a hard cutoff instead of an algebraic decay predicted by LB’s theory.https://www.mdpi.com/1099-4300/25/10/1379long rangeLynden-bellMonte Carlocore halo |
| spellingShingle | Tarcísio N. Teles Calvin A. F. Farias Renato Pakter Yan Levin A Monte Carlo Method for Calculating Lynden-Bell Equilibrium in Self-Gravitating Systems Entropy long range Lynden-bell Monte Carlo core halo |
| title | A Monte Carlo Method for Calculating Lynden-Bell Equilibrium in Self-Gravitating Systems |
| title_full | A Monte Carlo Method for Calculating Lynden-Bell Equilibrium in Self-Gravitating Systems |
| title_fullStr | A Monte Carlo Method for Calculating Lynden-Bell Equilibrium in Self-Gravitating Systems |
| title_full_unstemmed | A Monte Carlo Method for Calculating Lynden-Bell Equilibrium in Self-Gravitating Systems |
| title_short | A Monte Carlo Method for Calculating Lynden-Bell Equilibrium in Self-Gravitating Systems |
| title_sort | monte carlo method for calculating lynden bell equilibrium in self gravitating systems |
| topic | long range Lynden-bell Monte Carlo core halo |
| url | https://www.mdpi.com/1099-4300/25/10/1379 |
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