Abstract
We investigate the energy nonadditivity relationship E(A∪B) = E(A) + E(B) + αE(A)E(B) which is often considered in the development of the statistical physics of nonextensive systems. It was recently found that α in this equation was not constant for a given system in a given situation and could not characterize nonextensivity for that system. In this work, we select several typical nonextensive systems and compute the behavior of α when a system changes its size or is divided into subsystems in different fashions. Three kinds of interactions are considered. It is found by a thought experiment that α depends on the system size and the interaction as expected and on the way we divide the system. However, one of the major results of this work is that, for given system, α has a minimum with respect to division position. Around this position, there is a zone in which α is more or less constant, a situation where the sizes of the subsystems are comparable. The width of this zone depends on the interaction and on the system size. We conclude that if α is considered approximately constant in this zone, the two mathematical difficulties raised in previous studies are solved, meaning that the nonadditive relationship can characterize the nonadditivity of the system as an approximation. In all the cases, α tends to zero in the thermodynamic limit (N→∞) as expected.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Terletskii Y P. Statistical Physics. Amsterdam: North-Holland, 1971
Ha M, Li Y, Li J, et al. The key theorem and the bounds on the rate of uniform convergence of learning theory on Sugeno measure space. Sci China Ser F-Inf Sci, 2006, 49: 372–385
Liu S, Yang X, Yang Z. Modification of free-energy density functional theory approach for prediction of high-pressure mixture adsorption. Chinese Sci Bull, 2008, 53: 1358–1364
Tsallis C. Nonadditive entropy and nonextensive statistical mechanics-An overview after 20 years. Braz J Phys, 2009, 39: 337–356
Ou C J, Li W, Tsobnang F, et al. Possible canonical distributions for finite systems with nonadditive energy. Physica A, 2008, 387: 5761–5767
Wang Q A, Nivanen L, Mehaute A Le, et al. Temperature and pressure in nonextensive thermostatistics. Europhys Lett, 2004, 65: 606–612
Li W, Wang Q A, Nivanen L, et al. On different q-systems in nonextensive thermostatistics. Eur Phys J B, 2005, 48: 95–100
Tsallis C, Tirnakli U. Nonadditive entropy and nonextensive statistical mechanics-Some central concepts and recent applications. J Phys Conf Ser, 2010, 201: 1–15
Wang Q A, Ou C J, Chen J C. The q-nonadditivity of nonextensive statistics is not a true physical property. arXiv: 0910.3826v2
Chavanis P H, Campa A. Inhomogeneous Tsallis distributions in the HMF model. Eur Phys J B, 2010, 76: 581–611
Author information
Authors and Affiliations
Corresponding authors
Additional information
This article is published with open access at Springerlink.com
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Wang, R., Nganso Djanteng, S., Ei Kaabouchi, A. et al. Investigation of an energy nonadditivity for nonextensive systems. Chin. Sci. Bull. 56, 3661–3665 (2011). https://doi.org/10.1007/s11434-011-4676-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11434-011-4676-8