Question

Let $p(\bar{p}, \bar{q}, t)$ be the phase space density of an ensemble of a system. The Hamiltonian of the system is $H(p, q)$. If $\\{A, B\\}$ denotes the Poisson bracket of $A$ and $B$, then $\frac{dp}{dt} = 0$ implies

• A. $\frac{dp}{dt} = 0$
• B. $\frac{dp}{dt} \propto \\{p, H\\}$
• C. $\frac{dp}{dt} \propto \\{p, \frac{\bar{p} .\bar{q}}{2}\\}$
• D. $\frac{dp}{dt} \propto \\{p, \frac{\bar{q} .\bar{q}}{2}\\}$

Answer 1

Answer: (B)

$\frac{dp}{dt} \propto \\{p, H\\}$

Answer 2

The correct option is (B) :( \frac{dp}{dt} \propto \{p, H\} \