Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Identifying quantum subsystems using Clausius' second law of
  thermodynamics   There are many ways to decompose the Hilbert space H of a composite quantum
system into tensor product subspaces. Different subsystem decompositions
generally imply different interaction Hamiltonians V, and therefore different
expectation values for subsystem observables. This means that thE uniqueness of
physical predictions is not guaranteed, despite the uniqueness of the total
Hamiltonian H and the total Hilbert space. Here we use Clausius' version of the
second law of thermodynamics (CSL) and standard identifications of
thermodynamic quantities to identify possible subsystem decompositions. It is
shown that agreement with the CSL is obtained, whenever the total Hamiltonian
and the subsystem-dependent interaction Hamiltonian commute (i.e. [H,V]=0). Not
imposing this constraint can result in the transfer of heat from a cooler to a
hotter subsystem, in conflict with thermodynamics. We also investigate the
status of the CSL with respect to non- standard definitions of thermodynamic
quantities and quantum subsystems.

24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol