Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropy of probability kernels from the backwards tail boundary   A number of recent works have sought to generalize the Kolmogorov-Sinai
entropy of probability-preserving transformations to the setting of Markov
operators acting on the integrable functions on a probability space $(X,\mu)$.
These have culminated in a proof by Downarovicz and Frej that these definitions
all coincide, and that the resulting quantity is uniquely characterized by
certain properties.
  On the other hand, Makarov has shown that this `operator entropy' is always
dominated by the Kolmogorov-Sinai entropy of a classical system that may be
constructed from a Markov operator, and that these numbers coincide under
certain extra assumptions. This note proves that equality in all cases.

16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int