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Nonextensive thermodynamic relations based on the assumption of temperature duality

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Abstract

The nonextensive thermodynamic relations are expressed under the assumption of temperature duality, endowing the “physical temperature” and the “Lagrange temperature” in different physical senses. Based on this assumption, two sets of parallel Legendre transform structures are given. One is called “physical” set, and the other is called “Lagrange” set. In these two formalisms, the thermodynamic quantities and the thermodynamic relations are both liked through the Tsallis factor. Application of the two sets of the thermodynamic relations to the self-gravitating system shows that the heat capacity defined in the classical thermodynamics has no relevance to the stability of the system. Instead, the newly defined heat capacity can determine the stability of the system.

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Authors and Affiliations

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

    Yahui Zheng & Jiulin Du

  2. Department of Physics, School of Science, Qiqihar University, Qiqihar City, 161006, China

    Yahui Zheng

Authors
  1. Yahui Zheng
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  2. Jiulin Du
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Correspondence to Jiulin Du.

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Communicated by Andreas Öchsner.

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Zheng, Y., Du, J. Nonextensive thermodynamic relations based on the assumption of temperature duality. Continuum Mech. Thermodyn. 28, 1791–1805 (2016). https://doi.org/10.1007/s00161-016-0510-5

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  • DOI: https://doi.org/10.1007/s00161-016-0510-5

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