  The experimental confirmation of Landauer principle and the emerging concept
of a computational universe make it more and more crucial to understand the
physical sense of information, as it has an intrinsic relation with observer
knowledge that is often rejected as subjective. In this paper we propose an
objective definition of phase information in a purely classical computational
universe with quantized phase states, this quantization being imposed by our
fundamental hypothesis that physical information has a finite and limited
density, responsible for the irreversibility. We use a statistical study of
results obtained by numerical simulations of a billiard to highlight an
excessive and paradoxical loss of phase information that we solve by involving
a classical to quantum transition. After discussing the pertinence of such a
transition to clarify some problematic aspects of statistical physics, we
conclude that a computational universe should automatically lose phase
information through time in an irreversible way, which could be compensated by
a gain of physical information due to observation and decoherence.
