Presented at the New Swiss Chemical Society (NSCS) Fall Meeting, Universite de Lausanne, 15 October 1997.
(Abstract published in Chimia, 1997, 51, 646)

Physical Chemistry, Poster 231

Negative and Positive Temperatures of Static and Dynamic Aspects

Shu-Kun Lin

Molecular Diversity Preservation International (MDPI)
Sängergasse 25, CH-4054 Basel (e-mail:

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.