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

The Correct Option is B

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