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An important condition of a tests on the Bell inequality is that there are no statistical correlations between the choices of measurement settings between measurement sites. Typically this is achieved by a pair of quantum random number generators that are spacelike separated. These setups leave a potential loophole in which an unknown cause can effect the setting choices. To circumvent this loophole researchers in Vienna used distant astronomical sources to control the measurement settings within their Bell test.
As stated by the second law of thermodynamics, the entropy produced by irreversible processes keeps increasing until the system reaches equilibrium, and this entropy production rate is always non-negative. But when some quantum properties, e.g., quantum coherence or squeezing, exist in the bath, the conventional description of the entropy production rate does not apply, and its positivity is no longer guaranteed. We notice that the entropy production rate can be generalized to be the increasing rate of the mutual information between the open system and its environment. For thermal baths, this mutual information production rate could reduce to the previous entropy production rate. For non-thermal baths, in an example of a single boson mode contacted with multiple squeezed thermal baths, we proved that the mutual information production rate is always non-negative. The monotonic increasing mutual information means the system and its environment are becoming more and more correlated before they reach the equilibrium.
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