  The second law of thermodynamics states that entropy increases (or does not
change) by time in an isolated system. As microscopic physical laws are
reversible, the origin of irreversibility is not straightforward. Although the
outcome of a measurement on a pure quantum state is not fully predictable due
to the Heisenberg uncertainty principle, quantum and finite entropy
uncertainties are thought to be fundamentally different. We propose to
calculate the predictability of measurements comprising both quantum and
entropic uncertainties. We show that the unpredictability of measurements is
identical to entropy in case of semiclassical statistical mechanics, and it
increases by time in a pure entangled quantum state as a result of quantum
measurement.
