Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal geometric approach to uncertainty, entropy and information   It is shown that for any ensemble, whether classical or quantum, continuous
or discrete, there is only one measure of the "volume" of the ensemble that is
compatible with several basic geometric postulates. This volume measure is thus
a preferred and universal choice for characterising the inherent spread,
dispersion, localisation, etc, of the ensemble. Remarkably, this unique
"ensemble volume" is a simple function of the ensemble entropy, and hence
provides a new geometric characterisation of the latter quantity. Applications
include unified, volume-based derivations of the Holevo and Shannon bounds in
quantum and classical information theory; a precise geometric interpretation of
thermodynamic entropy for equilibrium ensembles; a geometric derivation of
semi-classical uncertainty relations; a new means for defining classical and
quantum localization for arbitrary evolution processes; a geometric
interpretation of relative entropy; and a new proposed definition for the
spot-size of an optical beam. Advantages of the ensemble volume over other
measures of localization (root-mean-square deviation, Renyi entropies, and
inverse participation ratio) are discussed.

21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph