Full Statistics of Regularized Local Energy Density in a Freely Expanding Kipnis-Marchioro-Presutti Gas
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916493599440896 |
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| author | Bettelheim, Eldad Meerson, Baruch |
| author_facet | Bettelheim, Eldad Meerson, Baruch |
| contents | We combine the Macroscopic Fluctuation Theory and the Inverse Scattering Method to determine the full long-time statistics of the energy density $u(x,t)$ averaged over a given spatial interval, $$U =\frac{1}{2L}\int_{-L}^{L}dx\, u(x,t),$$ in a freely expanding Kipnis-Marchioro-Presutti (KMP) lattice gas on the line, following the release at $t=0$ of a finite amount of energy at the origin. In particular, we show that, as time $t$ goes to infinity at fixed $L$, the large deviation function of $U$ approaches a universal, $L$-independent form when expressed in terms of the energy content of the interval $|x|<L$. A key part of the solution is the determination of the most likely configuration of the energy density at time $t$, conditional on $U$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06335 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Full Statistics of Regularized Local Energy Density in a Freely Expanding Kipnis-Marchioro-Presutti Gas Bettelheim, Eldad Meerson, Baruch Statistical Mechanics We combine the Macroscopic Fluctuation Theory and the Inverse Scattering Method to determine the full long-time statistics of the energy density $u(x,t)$ averaged over a given spatial interval, $$U =\frac{1}{2L}\int_{-L}^{L}dx\, u(x,t),$$ in a freely expanding Kipnis-Marchioro-Presutti (KMP) lattice gas on the line, following the release at $t=0$ of a finite amount of energy at the origin. In particular, we show that, as time $t$ goes to infinity at fixed $L$, the large deviation function of $U$ approaches a universal, $L$-independent form when expressed in terms of the energy content of the interval $|x|<L$. A key part of the solution is the determination of the most likely configuration of the energy density at time $t$, conditional on $U$. |
| title | Full Statistics of Regularized Local Energy Density in a Freely Expanding Kipnis-Marchioro-Presutti Gas |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2407.06335 |