Towards parallel computing: representation of a linear finite state digital logic machine by a molecular relaxation process

A chemical system displaced not far from equilibrium is shown to offer a physical realization of a linear sequential digital logic machine. The requirement from the system is that its state is described by giving the current values of the concentration of different chemical species. The time evolution is therefore described by a classical master equation. The Landau-Teller process of vibrational relaxation of diatomic molecules in a buffer gas is used as a concrete example where each vibrational level is taken to be a distinct species. The probabilities (= fractional concentrations) of the species of the physicochemical system are transcribed as words composed of letters from a finite alphabet. The essential difference between the finite precision of the logic machine and the seemingly unbounded number of significant figures that could be used to specify a concentration is emphasized. The transcription between the two is made by using modular arithmetic that is, is the arithmetic of congruence. A digital machine corresponding to the vibrational relaxation process is constructed explicitly for the simple case of three vibrational levels. In this exploratory effort we use words of only one letter. Even this is sufficient to achieve an exponentially large number of memory states