Question

Is it possible to derive Liouville's Theorem purely from maximum differential entropy?

Answer 1

Hey mate ^_^

Typically in physics (at least the way I learned mechanics), this is derived using the multi-dimensional divergence theorem on the 2N2N-dimensional phase space...


#Be Brainly❤️

Answer 2

Hello mate here is your answer.

Typically in physics (at least the way I learned mechanics), this is derived using the multi-dimensional divergence theorem on the 2N2N-dimensional phase space i.e.

0=∂tρ+∑i=1N(∂(ρqi˙)qi+∂(ρpi˙)pi)0=∂tρ+∑i=1N(∂(ρqi˙)qi+∂(ρpi˙)pi),

and the terms in brackets are simplified using Hamiltonian equation of motion to obtain Liouville's Theorem:

dρdt=∂ρ∂t+∑i(∂ρ∂qiqi˙+∂ρ∂pipi˙)=0dρdt=∂ρ∂t+∑i(∂ρ∂qiqi˙+∂ρ∂pipi˙)=0.

Hope it helps you.