This operation relates the external protocols in the numerator and denominator of the Crooks relation. In stochastic thermo, the entropy production is proportional to the log of the following: the probability of a trajectory, over the probability of the trajectory under this operation. In quantum mechanics, this operation is an anti-unitary operator that [emphasize] commutes with the Hamiltonian. (15[1])Spin-1/2 systems that are invariant under this operation (-5[1])satisfy (*) Kramers’ theorem. Magnetic fields break symmetry under this operation, which is unified with symmetry under charge conjugation and parity inversion. Loschmidt’s paradox asks how it is possible for Newton’s laws, which are invariant under this operation, to give rise to a quantity like entropy that only increases. For 10 points, name this operation analogized to playing a movie backwards. (10[1])■END■