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MacIntyre, Duncan

When a small perturbation λVˆ is added to a Hamiltonian Hˆ 0, the Von Neumann entropy of a subsystem may change as a result. I study this change in entropy. In particular, I derive a general expression for the change in entropy based on perturbative corrections to the eigenvalues of the reduced density operator. It shows that the entropy of a mixed state will never decrease provided (1) there exist component states with zero initial probability that can be transitioned into and (2) initial component states do not have lower-order corrections to their probabilities than states with zero initial probability. I also derive an expression for the change in entropy for what I call “diagonally separable states” (which include product states) that can transition into states with zero initial probability in the accessible space. For such systems, the change in entropy depends only on the transition amplitudes to states with zero initial probability. I consider two simple examples applying my results and speculate on future directions.

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University of British Columbia. PHYS 449

Vancouver : University of British Columbia Library

10.14288/1.0445041

Science, Faculty of; Mathematics, Department of; Physics and Astronomy, Department of

Undergraduate

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