Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological supersymmetry breaking: Definition and stochastic
  generalization of chaos and the limit of applicability of statistics   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
initial-conditions-independent probability distributions. As a result, the
definitive assumption of physical statistics that the ground state is a
steady-state total probability distribution is not valid for chaotic SDEs.

13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an