in a series of notes published in Nature during the years 1956-1958, K. R. Popper 1 has expounded his thesis of the “untenability of the widespread, though surely not universal, belief that the ‘arrow of time’ is closely connected with, or dependent upon, the law that disorder (entropy) tends to increase.” (II) Specifically, he argues in the first three of his four notes that there exist irreversible processes in nature whose irreversibility does not depend on their involvement of an entropy increase. Instead, their irreversibility is nomologically contingent in the following sense: the laws of nature governing elementary processes do indeed allow the temporal inverses of these irreversible processes, but these processes are de facto irreversible, because the spontaneous concatenation of the initial conditions requisite for the occurrence of their temporal inverses is well-nigh physically impossible. Noting that “Although the arrow of time is not implied by the fundamental equations [laws governing elementary processes], it nevertheless characterizes most solutions” (I), Popper therefore rejects the claim that “every non-statistical or ‘classical’ mechanical process is reversible” (IV). In the fourth of his communications, he maintains against Boltzmann that the statistical behavior of the entropy of physical systems not only fails to be the sole physical basis for the anistropy of time, but does not qualify at all as such a basis. 2 For Popper argues that, if it did, the temporal description of fluctuation phenomena would entail absurdities of several kinds.