Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Necessary and Sufficient Condition on the Lindblad Equation to Prevent
  Entropy Increase   It is shown that in order for the solutions of the Lindblad equation never to
give a decreasing von Neumann entropy, it is necessary and sufficient that the
operators appearing in this equation should be unitary linear combinations of
their adjoints. In this case, these operators may be replaced with Hermitian
operators, without changing the evolution of density matrices.

22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an