  Emergence of deterministic and irreversible macroscopic behavior from
deterministic and reversible microscopic dynamics is understood as a result of
the law of large numbers. In this paper, we prove on the basis of the theory of
algorithmic randomness that Martin-L\"of random initial microstates satisfy an
irreversible macroscopic law in the Kac infinite chain model. We find that the
time-reversed state of a random state is not random as well as violates the
macroscopic law.
