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Thermodynamic stability criterion and fluctuation theory in nonextensive thermodynamics

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Abstract

We have constructed a nonextensive thermodynamic formalism consisting of two sets of parallel Legendre transformation structures in previous papers. One is the physical set and the other is the Lagrange set. In this paper, we study the thermodynamic stability criterion with a dual interpretation of the thermodynamic relations and quantities. By recourse to the assumption that volume in nonextenstive system is nonadditive, we conclude that it is the physical pressure that is responsible for the mechanical balance between any two parts in a given nonextensive system. It is verified that in the physical set of transformation structures, the stability criterion can be expressed in terms of heat capacity and isothermal compressibility. We also discuss the fluctuation theory in nonextensive thermodynamics.

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Authors and Affiliations

  1. Department of Electronics and Communication Engineering, Henan Institute of Technology, Xinxiang, 453003, China

    Yahui Zheng

  2. Department of Physics, School of Science, Tianjin University, Tianjin, 300072, China

    Jiulin Du

  3. Department of Physics, School of Science, Qiqihar University, Qiqihar, 161006, China

    Yahui Zheng & Faku Liang

Authors
  1. Yahui Zheng
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  2. Jiulin Du
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  3. Faku Liang
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Correspondence to Jiulin Du.

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Communicated by Andreas Öchsner.

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Zheng, Y., Du, J. & Liang, F. Thermodynamic stability criterion and fluctuation theory in nonextensive thermodynamics. Continuum Mech. Thermodyn. 30, 629–639 (2018). https://doi.org/10.1007/s00161-018-0628-8

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  • DOI: https://doi.org/10.1007/s00161-018-0628-8

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