Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (4): 40501-040501.doi: 10.1088/1674-1056/22/4/040501

• GENERAL • 上一篇    下一篇

Incomplete nonextensive statistics and the zeroth law of thermodynamics

黄志福a b, 欧聪杰a, 陈金灿b   

  1. a College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China;
    b Department of Physics, Xiamen University, Xiamen 361005, China
  • 收稿日期:2012-08-02 修回日期:2012-09-06 出版日期:2013-03-01 发布日期:2013-03-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11005041), the Natural Science Foundation of Fujian Province, China (Grant No. 2010J05007), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China (Grant No. 2010-1561), the Basic Science Research Foundation, China (Grant No. JB-SJ1005), and the Science Research Fund of Huaqiao University, China (including the support for Huang (Grant No. 11BS207)).

Incomplete nonextensive statistics and the zeroth law of thermodynamics

Huang Zhi-Fu (黄志福)a b, Ou Cong-Jie (欧聪杰)a, Chen Jin-Can (陈金灿)b   

  1. a College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China;
    b Department of Physics, Xiamen University, Xiamen 361005, China
  • Received:2012-08-02 Revised:2012-09-06 Online:2013-03-01 Published:2013-03-01
  • Contact: Chen Jin-Can E-mail:jcchen@xmu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11005041), the Natural Science Foundation of Fujian Province, China (Grant No. 2010J05007), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China (Grant No. 2010-1561), the Basic Science Research Foundation, China (Grant No. JB-SJ1005), and the Science Research Fund of Huaqiao University, China (including the support for Huang (Grant No. 11BS207)).

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摘要： On the basis of the entropy of incomplete statistics (IS) and the joint probability factorization condition, two controversial problems existing in IS are investigated: one is what expression of the internal energy is reasonable for a composite system and the other is whether the traditional zeroth law of thermodynamics is suitable for IS. Some new equivalent expressions of the internal energy of a composite system are derived through accurate mathematical calculation. Moreover, a self-consistent calculation is used to expound that the zeroth law of thermodynamics is also suitable for IS, but it cannot be proven theoretically. Finally, it is pointed out that the generalized zeroth law of thermodynamics for incomplete nonextensive statistics is unnecessary and the nonextensive assumptions for the composite internal energy will lead to mathematical contradiction.

关键词: classical statistical mechanics, thermodynamics, probability theory

Abstract: On the basis of the entropy of incomplete statistics (IS) and the joint probability factorization condition, two controversial problems existing in IS are investigated: one is what expression of the internal energy is reasonable for a composite system and the other is whether the traditional zeroth law of thermodynamics is suitable for IS. Some new equivalent expressions of the internal energy of a composite system are derived through accurate mathematical calculation. Moreover, a self-consistent calculation is used to expound that the zeroth law of thermodynamics is also suitable for IS, but it cannot be proven theoretically. Finally, it is pointed out that the generalized zeroth law of thermodynamics for incomplete nonextensive statistics is unnecessary and the nonextensive assumptions for the composite internal energy will lead to mathematical contradiction.

Key words: classical statistical mechanics, thermodynamics, probability theory

中图分类号:  (Classical statistical mechanics)

  • 05.20.-y
05.70.-a (Thermodynamics) 02.50.-r (Probability theory, stochastic processes, and statistics)