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# The question is on Statistical Mechanics, Kinetic Theory: Poisson Brackets:

The question is on Statistical Mechanics, Kinetic Theory:

Poisson Brackets:

(a) Show that for observable O(p(x),q(x)), dO/dt={O,H}, along the time trajectory of any micro state, where H is the Hamiltonian.

(b) If the ensemble average <{O,H}> =0 for any observable O(p,q) in phase space, show that the ensemble density satisfies {H,p}=0.

The question is totally valid stat. mech. question, and there are no extra components or anything missing. The question does not belong to me. It is given on the following webpage: http://web.mit.edu/8.333/www/problems/PS3.pdf I want to understand how it can be solved. If you do not know how it is solved please stop flagging my question and leave it to the people who may help me. Thank you.