3.6 Does entropy increase in quantum systems?. (Mathematics, Quan) 3 One can show (Exercise (5.7) in...
3.6 Does entropy increase in quantum systems?. (Mathematics, Quan) 3 One can show (Exercise (5.7) in my text, 'Entropy, Order Parameters, and Complex ity') that in classical Hamiltonian systems the non-equilibrium entropy Snonequil -kBĪp log ρ is constant in a classical mechanical Hamiltonian system. Here you will show that in the microscop system, the entropy is also time independent, even for general, time-dependent density matrices p(t) Using the evolution law op/it-[H,คั(ih), prove that S--Tr(plogp) is tirne independent, where ρ is any density matri. (Hint: Go to an orthonormal basis ψί which diagonalizes ρ. Show that (t) is also orthonormal, and take the trace in that basis. Use the cyclic invariance of the trace,) ic evolution of an isolated quantum