Fermi statistics method applied to model macroscopic demographic data

The study begins by considering an abstract object (cellular automaton) able of moving -- by arbitrary decision -- between two given fixed positions. That is, at each clock step, it can change position or remain stationary in its current position. This object, which we call an Arbitrary Oscillator (ArbO), cannot evolve indefinitely since it may encounter 'end-of-life' events, which are also random. If we place quantitative limits on the number of arbitrary events and impose that the life cycle of ArbO must end in any case, we can use Fermi statistics to find the most probable distribution of fatal events along the possible sequences of choices. This distribution is represented by a recursive function that can be calculated for each total number of possible 'life/death' choices, which we will call Total Cases (TC). By means of a time-scale adjustment, we have associated the distribution curves of ArbO 'fatal' events with the demographic mortality curves (dx and qx data) of populations in the case of Italy. To better study the properties of the statistical function thus found, we attempted a continuous transposition of the recursive equation, seeking solutions to the differential equation linkable with it. With a continuous analytical expression, the characteristics of this statistical distribution can be studied more effectively. Similarities and differences with demographic mortality curves have been highlighted, attempting to explain the latter as overlaps of curves with different TC parameters. Implications with life span and more general life cycle concepts are outlined. A correlation with a more recent study using a multi-omics approach is also pointed out. Key Words: Cellular Automata, Fermi Statistics, Logistic Distribution, Demographic Mortality, Lifespan