1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Theorems of Liouville and Poincare & their relation to entropy

  1. Oct 4, 2008 #1
    If we have a system for which the Liouville's tm holds, can we automaticly say the Poincare's recurrence tm also holds? Presumably this is true in microcanonical ansable, but how about canonical, where the energy isn't constant?
  2. jcsd
  3. Oct 4, 2008 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    Poincaré's recurrence theorem holds for any statistical system in which system's energy and the system's space do not change. It says, essentially, that such a system will return to a microstate that is to within an arbitrarily close approximation of its original microstate, if it is given enough time. So if energy is not conserved in the system, Poincaré's recurrence theorem does not hold.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Theorems Liouville Poincare Date
I Liouville's theorem Nov 10, 2016
Challenging Susskind's uncompressible flow in Liouville’s Theorem Oct 19, 2013
Liouville's theorem and atom optics May 4, 2012
Question on liouville's theorem Feb 26, 2010
Liouville's theorem Oct 4, 2009