Enhanced violation of a Leggett-Garg inequality under nonequilibrium thermal conditions

Abstract: We investigate both analytically and numerically violations of a Leggett-Garg inequality (LGI) for a composite quantum system in contact with two separate reservoirs at different temperatures. Remarkably we find that LGI violations can be enhanced when a heat current is established at low temperatures in a steady-state regime. Based on a Kraus operator decomposition of the non-unitary evolution for a system formed by two interacting spins or quantum bits, we provide analytical support for power law relations between dissipation strength and mean temperature in the borderlines separating parameter regions where non-equilibrium conditions affect differently the maximal LGI violation. Furthermore, a correspondence between spatial and temporal correlation inequalities is shown to persist even in such nonequilibrium thermal settings.