Journal of Physical Chemistry B, Vol.108, No.49, 18980-18987, 2004
Nonextensive approach to thermodynamics: Analysis and suggestions, and application to chemical reactivity
In microscopic heterogeneous reaction media, such as drops, fogs, porous substrates, micellar solutions, interpenetrated phases, chemical reactivity depends, in some cases, not only on the nature and the proportion of reactants but also on the shape, the size, and the structure of the system. This kind of behavior cannot be described in the strict framework of classical thermodynamics using extensive state functions. Physicists have shown that it is possible to extend the application field of thermodynamics to this kind of problem by using nonextensive state functions. Thus, by a statistical approach, C. Tsallis proposed a nonextensive form of the entropy which involves a fractal dimension. Although the suggested functions are interesting from a fundamental point of view, they are often difficult for the chemist to exploit. Therefore, we have attempted to tackle this problem in another way and propose a generalization of the rules of classical thermodynamics so that they can be adapted to the description of chemical reactivity in complex media. Thus, to allow the state functions to have the possibility of being or not being extensive, we propose the assumption that the state functions can be Euler's functions of the system mass with a homogeneity order, m, other than 1. For m = 1, the rules of classical thermodynamics apply. The state functions will be named "superextensive" for m > 1, and "subextensive" for m < 1. We describe the justification and consequences of these conventions and their application to chemical reactivity. The rule of additivity of the nonextensive entropy obtained by our approach is similar to that proposed by C. Tsallis.