Flow of a statistical ensemble in the potential x**6 + 4*x**3 - 5*x**2 - 4*x. Over long times it becomes swirled up, and appears to become a smooth and stable distribution. However, this stability is an artifact of the pixelization (the actual structure is too fine to perceive).<br>This animation is inspired by a discussion of Gibbs in his 1902 <a href="https://en.wikisource.org/wiki/Elementary_Principles_in_Statistical_Mechanics" class="extiw" title="wikisource:Elementary Principles in Statistical Mechanics">wikisource:Elementary Principles in Statistical Mechanics</a>, Chapter XII, p. 143: "Tendency in an ensemble of isolated systems toward a state of statistical equilibrium".
A quantum version of this can be found at <a href="//commons.wikimedia.org/wiki/File:Hamiltonian_flow_quantum.webm" title="File:Hamiltonian flow quantum.webm">File:Hamiltonian flow quantum.webm</a>
<a href="//commons.wikimedia.org/wiki/User:Nanite" title="User:Nanite">Nanite</a>
2013-10-27 00:06:21
<span class="int-own-work" lang="en">Own work</span>