Thermodynamic Limit and Stability

  • Giovanni Gallavotti
Part of the Texts and Monographs in Physics book series (TMP)


The stability and temperedness conditions (see (2.2.17), (2.2.18)):
$$\begin{array}{l}\Phi (\underline q ) = \sum\limits_{i < j} {\varphi ({{\underline q }_i} - {{\underline q }_j}) \ge - BN} \quad stability \\\left| {\varphi (\underline q - \underline {q'} )} \right| \le C{\left| {\underline q - \underline {q'} } \right|^{ - 3 - \varepsilon }}\;for\;\left| {\underline q - \underline {q'} } \right| \ge {r_0}\;temperedness \\\end{array}$$
for suitable constants C > 0, ε > 0, r 0 > 0, have to be imposed on the interaction potential in order to insure the existence of the limits in (2.3.8), (2.3.9) or (2.5.12) defining f c, sm or pgc, respectively, i. e. the thermodynamic functions associated with the partition functions of various orthodic ensembles. The conditions are particularly interesting because, besides the above mathematical role, they have a simple, and profound, physical meaning.


Partition Function Thermodynamic Limit Hard Core Canonical Ensemble Classical Ensemble 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Giovanni Gallavotti
    • 1
  1. 1.Dipartimento di FisicaUniversità degli Studi di Roma “La Sapienza”RomaItaly

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