Irreversibility and Space-Time Structure

Abstract

I am happy to participate in this conference dealing with fluctuations and sensitivity. One of the main outcomes of research in macroscopic physics over the last decades is that we live in a pluralistic universe; we deal both with dissipative systems and with conservative systems [1] (I limit myself here to classical dynamical systems). Dissipative and conservative systems have widely different properties. Briefly, dissipative systems are characterized by asymptotic stability. They forget temporary perturbations. The simplest example, well known to everybody, is a pendulum with friction. If perturbed it goes back to the equilibrium position. This equilibrium position is a point attractor. However, we know now that attractors may be more complicated than isolated points. They may be lines in phase space, such as in periodic chemical reactions or even more complicated mathematical objects like fractals. That is why we speak today of strange attractors. The second common element in dissipative systems is the dissymmetry in respect to time. All dissipative systems have a preferential direction of time; they progress towards their attractors for t going to +8 (and not for t going to −8). We could imagine a world in which some biological systems which belong to the class of dissipative systems would age while others become younger. In such a world some dissipative systems would tend to equilibrium for t→+8 while others do so for t→−8. But that is not our world, in which, so far as we know on empirical grounds, there is a universal time asymmetry.