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enricfemi
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form the proof in Hamiltonian, i didn't find any clue.
the problem is i can't understand it even i know how to prove it.
the problem is i can't understand it even i know how to prove it.
dx said:Liouville's theorem applies to all mechanical systems if you don't ignore degrees of freedom.
atyy said:Is this a correct expansion of what you are saying: Liouville's theorem says the phase space of a Hamiltonian system doesn't contract, so systems with attractors or dissipative systems can't be represented by Hamiltonians - but in principle the non-Hamiltonain behaviour comes from ignoring degrees of freedom?
No, Liouville's theorem can only be applied to conservative systems, meaning those in which energy is conserved. Dissipative systems involve energy loss, and therefore, Liouville's theorem cannot be applied.
Liouville's theorem is a fundamental law in physics that states the conservation of phase space volume in conservative systems. While it cannot be applied directly to dissipative systems, it can still be used in a modified form to study the behavior of these systems.
No, Liouville's theorem cannot be used to predict the behavior of dissipative systems. Dissipative systems involve energy loss, and therefore, their behavior cannot be predicted solely by the conservation of phase space volume.
Yes, there are limitations to applying Liouville's theorem to dissipative systems. As mentioned before, Liouville's theorem can only be applied to conservative systems, so it cannot be used directly in dissipative systems. However, it can still provide insights and be used in modified forms to study dissipative systems.
Yes, there have been efforts to extend Liouville's theorem to include dissipative systems. These extensions involve incorporating additional terms to the theorem to account for energy loss in dissipative systems. However, these extensions are still being researched and are not yet widely accepted in the scientific community.