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I've heard that non-equilibrium systems have the property that their phase space has a structure, as opposed to 'structure-less' phases spaces of equilibrium systems. What does this precisely mean? I'm not alluding to the symplectic structure of Hamiltonian systems, as many non-equilibrium systems are dissipative and therefore not Hamiltonian.

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    $\begingroup$ $\uparrow$ Heard where? $\endgroup$ – AccidentalFourierTransform May 7 '18 at 15:29
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    $\begingroup$ Consider this from the perspective of a micro-canonical system: In equilibrium all states on the submanifold the energy restricts to are equally likely, so the distribution in phase space is "featureless", in a non-equilibrium system there will be "features" in the sense, that not all states are equally likely. Similar statements will be possible about other ensembles (which can be though of as a part of a micro-canonical ensemble). $\endgroup$ – Sebastian Riese May 7 '18 at 15:44
  • $\begingroup$ Some dissipative systems approach attractor sets with fractal structure. Turbulence is one such phenomenon. The theory of chaos offers more examples. $\endgroup$ – Bert Barrois May 7 '18 at 18:50

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