  In this paper a viewpoint that time is an informational and thermal entity is
shown. We consider a model for a simple relaxation process for which a
relationship among event, time and temperature is mathematically formulated. It
is then explicitly illustrated that temperature and time are statistically
inferred through measurement of events. The probability distribution of the
events thus provides a mutual regulation between temperature and time, which
can relevantly be expressed in terms of the Fisher information metric. The
two-dimensional differential geometry of temperature and time then leads us to
a finding of a simple equation for the scalar curvature, R = -1, in this case
of relaxation process. This basic equation, in turn, may be regarded as
characterizing the nonequilibrium dynamical process and having a solution given
by the Fisher information metric. The time can then be interpreted so as to
appear in a thermal way.
