Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On The Correct Thermo-dynamic Potential for Electro-static Dielectric
  Energy   Various types of equilibrium processes involve electric fields. In some
cases, the electrical energy appears to be negative (e.g. if the voltage is
fixed by an external source). This paper explains how to derive the correct
thermo-dynamic potential for electro-static phenomena, whether the voltage is
fixed, or the charge is fixed, or some combination is fixed. In particular, we
explain, in complete detail, why fixing the voltage introduces "a minus sign"
in the electrical energy.
  Two explanations are given. The first explanation is based on a
lumped-parameter argument (i.e. a lumped-capacitor model). The second
explanation uses a distributed parameter model (i.e. a partial differential
equation (PDE) model) of a dielectric medium, in this case, we allow for
non-linearity and external polarization effects. Connections with Legendre
(duality) transforms are also discussed.

13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con