FIZIKA A 19 (2010) 4 , 171182
NEW CONSIDERATION ON COMPOSED NONEXTENSIVE MAGNETIC SYSTEMS
F. A. R. NAVARRO, M. S. REIS, E. K. LENZI and I. S. OLIVERA
Centro Brasilero de Pesquisa Físicas,
Rua Dr. Xavier Sigaud 150, Rio de Janeiro, 22290180, Brazil
Received 28 March 2010; Accepted 17 November 2010
Online 8 March 2011
In this paper, a composed A + B magnetic system, with
spins J_{A}=2 and J_{B}=3/2, is
considered within the meanfield approximation, in the
framework of Tsallis nonextensive statistics. Our motivation
is twofold: (1) to approach the existing experimental
data of manganese oxides (manganites), where Mn^{3+}
and Mn^{4+} form two magnetic sublattices, and (2)
to investigate the structure of nonextensive density
matrices of composed systems. By imposing that
thermodynamic quantities, such as the magnetization
of sublattices A and B, must be invariant whether
the calculation is taken over the total Hilbert
space or over partial subspaces, we found that the
expression for the nonextensive entropy must be
adapted. Our argument is supported by the calculation of
sublattice magnetizations M_{A} and M_{B},
internal energy, U_{A} and U_{B} and
magnetic specific heat, C_{A} and C_{B}.
It is shown that only with the modified entropy,
the two methods of calculation agree to each other.
Internal energy and magnetization are additive,
but no clear relationship was found between
S_{A}, S_{B} and the total entropy
S_{A+B} for q ≠ 1. It is shown that
the reason for the failure of the standard way
of calculation is the assumption of statistical
independence between the two subsystems, which
however does not affect the density matrix in
the full Hilbert space.
PACS numbers: 75.47.Lx, 05.90.+m
UDC 537.62, 537.611.4
Keywords: nonextensive statistical mechanics, manganites, partial trace
