Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thermodynamic equilibrium and its stability for Microcanonical systems
  described by the Sharma-Taneja-Mittal entropy   It is generally assumed that the thermodynamic stability of equilibrium state
is reflected by the concavity of entropy. We inquire, in the microcanonical
picture, on the validity of this statement for systems described by the
bi-parametric entropy $S_{_{\kappa, r}}$ of Sharma-Taneja-Mittal. We analyze
the ``composability'' rule for two statistically independent systems, A and B,
described by the entropy $S_{_{\kappa, r}}$ with the same set of the deformed
parameters. It is shown that, in spite of the concavity of the entropy, the
``composability'' rule modifies the thermodynamic stability conditions of the
equilibrium state. Depending on the values assumed by the deformed parameters,
when the relation $S_{_{\kappa, r}}({\rm A}\cup{\rm B})> S_{_{\kappa, r}}({\rm
A})+S_{_{\kappa, r}}({\rm B})$ holds (super-additive systems), the concavity
conditions does imply the thermodynamics stability. Otherwise, when the
relation $S_{_{\kappa, r}}({\rm A}\cup{\rm B})<S_{_{\kappa, r}}({\rm
A})+S_{_{\kappa, r}}({\rm B})$ holds (sub-additive systems), the concavity
conditions does not imply the thermodynamical stability of the equilibrium
state.

27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess