About a nonadditivity of energy and entropy
LUNAM Université, ISMANS, Laboratoire de Physique Statistique et
Systèmes Complexes, 44 avenue F.A.
2 College of Information Science and Engineering, Huaqiao University, Quanzhou 362021, P.R. China
3 Department of Physics, Xiamen University, Xiamen 361005, P.R. China
Received: 5 November 2011
Received in final form: 22 May 2012
Published online: 17 September 2012
The mathematical expression of nonadditivity X(1 ∪ 2) = X(1) + X(2) + αX(1)X(2) has been frequently used for the development of statistical physics for nonadditive system, where X is entropy or energy, and α is hoped to be a parameter characterising the nonadditive property of the composite system (1 ∪ 2). Here we show that this relationship cannot hold exactly. In general, α in this expression inevitably depends on how a given system with constant X(1 ∪ 2) is divided into subsystems 1 and 2. Hence mathematical problems may arise when it is used to characterise the nonadditivity of the system. Nevertheless, under some conditions, it is possible to use it as a good approximation.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2012