  The Leggett-Garg inequalities probe the classical-quantum boundary by putting
limits on the sum of pairwise correlation functions between classical
measurement devices that consecutively measured the same quantum system. The
apparent violation of these inequalities by standard quantum measurements has
cast doubt on quantum mechanics' ability to consistently describe classical
objects. Recent work has concluded that these inequalities cannot be violated
by either strong or weak projective measurements [1]. Here I consider an
entropic version of the Leggett-Garg inequalities that are different from the
standard inequalities yet similar in form, and can be defined without reference
to any particular observable. I find that the entropic inequalities also cannot
be be violated by strong quantum measurements. The entropic inequalities can be
extended to describe weak quantum measurements, and I show that these weak
entropic Leggett-Garg inequalities cannot be violated either even though the
quantum system remains unprojected, because the inequalities describe the
classical measurement devices, not the quantum system. I conclude that quantum
mechanics adequately describes classical devices, and that we should be careful
not to assume that the classical devices accurately describe the quantum
system.
