Topological supersymmetry breaking: The definition and stochastic generalization of chaos and the limit of applicability of statistics
Abstract
The concept of deterministic dynamical chaos has a long history and is well established by now. Nevertheless, its field theoretic essence and its stochastic generalization have been revealed only very recently. Within the newly found supersymmetric theory of stochastics (STS), all stochastic differential equations (SDEs) possess topological or de Rahm supersymmetry and stochastic chaos is the phenomenon of its spontaneous breakdown. Even though the STS is free of approximations and thus is technically solid, it is still missing a firm interpretational basis in order to be physically sound. Here, we make a few important steps toward the construction of the interpretational foundation for the STS. In particular, we discuss that one way to understand why the ground states of chaotic SDEs are conditional (not total) probability distributions, is that some of the variables have infinite memory of initial conditions and thus are not “thermalized”, i.e., cannot be described by the initialconditionsindependent probability distributions. As a result, the definitive assumption of physical statistics that the ground state is a steadystate total probability distribution is not valid for chaotic SDEs.
 Publication:

Modern Physics Letters B
 Pub Date:
 March 2016
 DOI:
 10.1142/S021798491650086X
 Bibcode:
 2016MPLB...3050086O
 Keywords:

 Stochastic dynamics;
 chaotic dynamics;
 supersymmetry