  A possible mechanism of time is formulated by developing an idea of time
replaced by quantum correlations, with the aid of modern quantum information
theory. We invent a microscopic model, where correlations of a closed system
are steadily read out as internal, quantum clocks that define time via their
relative phases. The model could realize emergent time evolutions which exhibit
unitarity of quantum theory, while its underlying process is driven
entropically. The key quantity turns out to be the amount of accessible
information about the clocks recording past events. By postulating the
so-called data-processing inequality (or strong subadditivity of entropy) as a
fundamental, physical limitation about how information decays, we propose that
conditional entropy about this past information should be constrained to be a
positive constant. The proposal implies a holographic property of this
conditional entropy in an analogous manner with the area law of entanglement
entropy.
