Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularities Unseen, Randomness Observed: Levels of Entropy Convergence   We study how the Shannon entropy of sequences produced by an information
source converges to the source's entropy rate. We synthesize several
phenomenological approaches to applying information theoretic measures of
randomness and memory to stochastic and deterministic processes by using
successive derivatives of the Shannon entropy growth curve. This leads, in
turn, to natural measures of apparent memory stored in a source and the amounts
of information that must be extracted from observations of a source in order
for it to be optimally predicted and for an observer to synchronize to it. One
consequence of ignoring these structural properties is that the missed
regularities are converted to apparent randomness. We demonstrate that this
problem arises particularly for small data sets; e.g., in settings where one
has access only to short measurement sequences.

21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph