Soluzioni alle domande degli esami di Solid State Physics - digitali (apple pencil)

The Gibbs Set Ensemble

The Gibbs set ensemble is a set of independent systems represented in different points of phase space, each with a density distribution function (coincided unless for a constant density distribution). As time goes by, the phase space motion of the gas resembles a collective interaction without collision but on any point. Using the "Lehman" description, we can write the equation of continuity for the gas as:

E(0D) + ∂p/∂t = 0

Writing in terms of p and q using Hamiltonian equations, we got:

∂p/∂t = -∂H/∂q

REMLIOUVILLE THEOSÈ iè since ∂p/∂t = 0, the distribution function is constant along any trajectory in the phase space.

IMPLICATI S: Since we assume the system to be deterministic, the trajectory behaves like an incompressible fluid.

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