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Thermodynamic Limit and Stability

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

Abstract

The stability and temperedness conditions (see (2.2.17), (2.2.18)):
$$\begin{array}{l}\Phi (\underline q ) = \sum\limits_{i < j} {\varphi ({{\underline q }_i} - {{\underline q }_j}) \ge - BN} \quad stability \\\left| {\varphi (\underline q - \underline {q'} )} \right| \le C{\left| {\underline q - \underline {q'} } \right|^{ - 3 - \varepsilon }}\;for\;\left| {\underline q - \underline {q'} } \right| \ge {r_0}\;temperedness \\\end{array}$$
(4.1.1)
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.

Keywords

Partition Function Thermodynamic Limit Hard Core Canonical Ensemble Classical Ensemble 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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