Entropy density and flux in topological and nonequilibrium quantum systems

We consider the flow of entropy and heat in quantum systems induced by topological fields and/or nonequilibrium bias conditions. A new solenoidal (divergence-free) contribution to the flow of entropy and heat is uncovered, which is missing from standard formulas for the heat current. This new term is shown to occur generically in such systems and to be large in magnitude in comparison to the conventional formulas. Although entropy is a nonlocal property in quantum mechanics, we show how to construct explicit expressions for the entropy density and entropy current density for systems of independent identical quantum particles, and apply these results to compute the flow of entropy in various model noninteracting systems, illustrating the importance of the new solenoidal contribution. Possible implications for the exchange of quantum information are discussed.