Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum-Mechanical Histories and the Uncertainty Principle:
  I.Information-Theoretic Inequalities   This paper is generally concerned with understanding how the uncertainty
principle arises in formulations of quantum mechanics, such as the decoherent
histories approach, whose central goal is the assignment of probabilities to
histories. We first consider histories characterized by position or momentum
projections at two moments of time. Both exact and approximate (Gaussian)
projections are studied. Shannon information is used as a measure of the
uncertainty expressed in the probabilities for these histories. We derive a
number of inequalities in which the uncertainty principle is expressed as a
lower bound on the information of phase space distributions derived from the
probabilities for two-time histories. We go on to consider histories
characterized by position samplings at $n$ moments of time. We derive a lower
bound on the information of the joint probability for $n$ position samplings.
Similar bounds are derived for histories characterized by samplings of other
variables. All lower bounds on the information of histories have the general
form $\ln \left( V_H / V_S \right) $, where $V_H$ is a volume element of
history space, which we define, and $V_S$ is the volume of that space probed by
the projections. We thus obtain a concise and general form of the uncertainty
principle referring directly to the histories description of the system, and
making no reference to notions of phase space.

37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph