# What is meant by “phase space structure”?

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.

• $\uparrow$ Heard where? – AccidentalFourierTransform May 7 '18 at 15:29
• 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). – Sebastian Riese May 7 '18 at 15:44
• Some dissipative systems approach attractor sets with fractal structure. Turbulence is one such phenomenon. The theory of chaos offers more examples. – Bert Barrois May 7 '18 at 18:50