Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extropy: Complementary Dual of Entropy   This article provides a completion to theories of information based on
entropy, resolving a longstanding question in its axiomatization as proposed by
Shannon and pursued by Jaynes. We show that Shannon's entropy function has a
complementary dual function which we call "extropy." The entropy and the
extropy of a binary distribution are identical. However, the measure bifurcates
into a pair of distinct measures for any quantity that is not merely an event
indicator. As with entropy, the maximum extropy distribution is also the
uniform distribution, and both measures are invariant with respect to
permutations of their mass functions. However, they behave quite differently in
their assessments of the refinement of a distribution, the axiom which
concerned Shannon and Jaynes. Their duality is specified via the relationship
among the entropies and extropies of course and fine partitions. We also
analyze the extropy function for densities, showing that relative extropy
constitutes a dual to the Kullback-Leibler divergence, widely recognized as the
continuous entropy measure. These results are unified within the general
structure of Bregman divergences. In this context they identify half the $L_2$
metric as the extropic dual to the entropic directed distance. We describe a
statistical application to the scoring of sequential forecast distributions
which provoked the discovery.

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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat