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- W2904019461 abstract "The time irreversibility and fast relaxation of collapsing $N$-body gravitating systems (as opposed to the time reversibility of the equations of motion for individual stars or particles) are traditionally attributed to information loss due to coarse-graining in the observation. We show that this subjective element is not necessary once one takes into consideration the fundamental fact that these systems are discrete, i.e. composed of a finite number $N$ of stars or particles. We show that a connection can be made between entropy estimates for discrete systems and the Nyquist-Shannon sampling criterion. Specifically, given a sample with $N$ points in a space of $d$ dimensions, the Nyquist-Shannon criterion constrains the size of the smallest structures defined by a function in the continuum that can be uniquely associated with the discrete sample. When applied to an $N$-body system, this theorem sets a lower limit to the size of phase-space structures (in the continuum) that can be resolved in the discrete data. As a consequence, the finite $N$ system tends to a uniform distribution after a relaxation time that typically scales as $N^{1/d}$. This provides an explanation for the fast achievement of a stationary state in collapsing $N$-body gravitating systems such as galaxies and star clusters, without the need to advocate for the subjective effect of coarse-graining." @default.
- W2904019461 created "2018-12-22" @default.
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- W2904019461 date "2019-02-06" @default.
- W2904019461 modified "2023-10-14" @default.
- W2904019461 title "The Discreteness-driven Relaxation of Collisionless Gravitating Systems: Entropy Evolution and the Nyquist–Shannon Theorem" @default.
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- W2904019461 doi "https://doi.org/10.3847/1538-4357/aaf8a7" @default.
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