(Abstract published in

Physical Chemistry, **Poster 231**

Shu-Kun Lin

Molecular Diversity Preservation International (MDPI)

Sängergasse 25,
CH-4054 Basel (e-mail: Lin@mdpi.org)

According to definition, total energy _{
}
and entropy _{
}
are both positive for any system. However, temperature _{
}
defined as _{
}
may be either positive or negative [1]. Following this definition and the
general criteria [1] for negative temperature, for any well-defined entropies
of any systems of hierarchical structures, correspondingly temperature(s) can
be defined, at least formally. We found that every system has symmetries of
*static* and *dynamic* aspects [2] and the two entropies and their
variations can be defined and in principle calculated according to _{
},
where _{
}
is the apparent symmetry number or the order of the group [2].

Therefore, for a conventional thermodynamic system, because information
registration involves reduced *static* symmetry (_{
})
[2] and the energy increase (_{
})
[3], a negative temperature _{
}
(s for static) can be formally defined, while the *dynamic* motion of such
system has a conventionally understood positive temperature _{
}
(d for dynamic).

Similarly, however, for a system of electronic motion in a single atom or a
molecule, the _{
}
of the local electronic *dynamic* motion is found to be negative with the
most negative value at the electronic ground state, while its local _{
}
of the *static *aspect of the electronic structure, such as spin parallel
orientation at excited states, is positive.

It is convenient to use these temperatures to characterize symmetry breaking phenomena at any one of many hierarchical structures in nature.

[1] a) N.F. Ramsey, *Phys. Rev*. **1956**, *103*, 20-28. b) C.
Kittel, H. Kroemer, *Thermal Physics*, Freeman, San Francisco, 1980.

[2] S.-K. Lin, *J. Chem. Inf. Comp. Sci.* **1996**, *36*, 367-376.
S.-K. Lin, *J. Theor. Chem.* **1996**, *1*, 135-150. S.-K. Lin,
*Theochem ***1997**, in press.

[3] W.G. Teich, G. Mahler, in: *Complexity, Entropy and the Physics of
Information*, W.H. Zurek (Ed.), Addison-Wesley, Redwood City, California,
1990, p.289.