Time Variable and Time Scales in Natural Systems and Their Modeling

In this chapter, I discuss the status of time when modeling natural systems. In such an operational perspective, time is defined and measured by a clock, i.e. the comparison with a given physical phenomenon. A central notion is that of time scales. I argue that the representation of time (e.g. discrete vs. continuous) is essentially a modeling choice, depending on the time scale of the observation or description compared to the characteristic times of the system. In integrated approaches developed for investigating systems presenting several levels of organization, it may be fruitful to consider several independent time variables describing evolution at different nested time scales (“multiple scale method”). This would solve some puzzling but recurrent statements, such as an evolution composed of a succession of equilibrium states, and leads to a practical understanding of diverse systems, from combustion and kinetic theory of gases in physics to enzymatic catalysis in biochemistry to adaptive dynamics in ecology. At a more fundamental level, the confrontation of descriptions performed at different scales and within different frameworks, from molecular dynamics to statistical mechanics to thermodynamics, is essential to delineate the limits of each of them, and overall reach a more informative understanding of reality. In particular, such a multi-scale confrontation offers a simple answer to the long-lasting opposition between microscopic reversibility and macroscopic irreversibility of isolated systems (the celebrated Second Principle of the thermodynamics). In biology, time scales are also essential in discussing the robustness of living systems and their evolutionary strategies.