Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonextensibility of internal energy in incomplete statistics and the
  zeroth law of thermodynamics   On the basis of the entropy of incomplete statistics (IS) and the joint
probability factorization condition, two controversial problems existing in IS
are investigated, where one is what the correct expression of the internal
energy for a composite system is and the other is whether the zeroth law of
thermodynamics is true or not. Some new equivalent expressions of the internal
energy of a composite system are derived through a precise mathematical
calculation. Moreover, a self-consistent calculation is used to expound that
the zeroth law of thermodynamics is also suitable for IS, but it can't be
proven from theory. Finally, it is pointed out that the generalized zeroth law
of thermodynamics and the expressions of the internal energy of a composite
system derived in literature are incorrect, because two irrational assumptions
have been implicitly introduced.

11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph