The concepts of the

quantity of heat

and

work

are deduced in the context of non-extensive statistical mechanics, following steps parallel to those employed in extensive statistical mechanics.
Keywords: heat - entropy - Kullback-Leibler relative entropy - Boltzmann-Gibbs and Tsallis approaches
Communicated by M. Sugiyama
Received: 31 January 2003, Accepted: 6 May 2003, Published online: 21 November 2003PACS:
05.70.-a, 05.30.-d, 05.90. + m