Journal of Applied Mathematics
Volume 2011 (2011), Article ID 804836, 7 pages
Research Article

Necessary and Sufficient Condition for Stability of Generalized Expectation Value

1Institut Supérieur des Matériaux et Mécaniques Avancés, 44 F. A. Bartholdi, 72000 Le Mans, France
2Department of Physical Engineering, Mie University, Mie 514-8507, Japan

Received 2 April 2011; Revised 21 June 2011; Accepted 23 June 2011

Academic Editor: Bernard Geurts

Copyright © 2011 Aziz El Kaabouchi and Sumiyoshi Abe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A class of generalized definitions of expectation value is often employed in nonequilibrium statistical mechanics for complex systems. Here, the necessary and sufficient condition is presented for such a class to be stable under small deformations of a given arbitrary probability distribution.