  We propose the entropic measurement-induced nonlocality (MIN) as the maximal
increment of von Neumann entropy induced by the locally non-disturbing
measurement, and study behaviors of it both in the independent and common
structured reservoirs. We present schemes for preserving the MIN, and show that
for certain initial states the MIN, including the quantum correlations, can
even be enhanced by the common reservoir. Additionally, we also show that the
different measures of MIN may give different qualitative characterizations of
nonlocal properties, i.e., it is rather measure dependent than state dependent.
