Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growing fluctuation of quantum weak invariant and dissipation   The concept of weak invariants has recently been introduced in the context of
conserved quantities in finite-time processes in nonequilibrium quantum
thermodynamics. A weak invariant itself has a time-dependent spectrum, but its
expectation value remains constant under time evolution defined by a relevant
master equation. Although its expectation value is thus conserved by
definition, its fluctuation is not. Here, time evolution of such a fluctuation
is studied. It is shown that if the subdynamics is given by a completely
positive map, then the fluctuation of the associated weak invariant does not
decrease in time. It is also shown, in the case of the Lindblad equation, how
the growth rate of the fluctuation is connected to the dissipator. As examples,
the harmonic oscillator with a time-dependent frequency and the spin in a
varying external magnetic field are discussed, and the fluctuations of their
Hamiltonians as the weak invariants are analyzed. Furthermore, a general
relation is presented for the specific heat and temperature of any subsystem
near equilibrium following the slow Markovian isoenergetic process.

11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org