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Thermodynamic Potentials Theory Aspects in External Differential Forms Calculus Representation

Received: 29 May 2017     Accepted: 28 June 2017     Published: 27 July 2017
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Abstract

Thorough review of external differential forms calculus basic theses presented. Potentialities of this mathematical discipline, which can describe physical properties of dielectric materials, magnets and photonic materials influenced by mechanical, thermal and electromagnetic factors more logically and objectively, then traditional methods, demonstrated. Methodological effectiveness of the differential forms of thermodynamic potentials application in the macroscopic properties of homogeneous mono- and polyvariant systems description has been demonstrated. The simple, fundamental, symmetrical to the thermodynamic variables choice relations demonstrating the calculus of differential forms benefits have been obtained. Using Pfaffian forms thermodynamics, have been demonstrated, that differential forms calculus application to a description of the physical reality allows to operate physical concepts at a deeper level, based on the fundamental physical and mathematical principles.

Published in Journal of Photonic Materials and Technology (Volume 3, Issue 2)
DOI 10.11648/j.jmpt.20170302.11
Page(s) 6-13
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

External Differential Forms, Thermodynamic Potentials, External Product, Maxwell’s Identity, Photonic Materials

References
[1] G. Grauert, I. Lib, V. Fisher. Differential and Integral Calculus. M.: World, 1971.
[2] B. Shuttz. Geometric methods of mathematical physics. M.: World, 1984.
[3] V. A. Ilyin, E. G. Poznyak. Fundamentals of mathematical analysis. V.2. M.: Science.
[4] F. Kleyn. Elementary mathematics from the point of view of the highest. V.2. Geometry. M.: Science, 1987.
[5] I. P. Bazarov. Thermodynamics. M.: Higher School, 1991.
[6] Yu. B. Rumer, M. Sh. Ryvkin. Thermodynamics, statistical physics and kinetics. M.: Science, 1972.
[7] V. K. Semenchenko. Selected Topics of Theoretical Physics. M.: Enlightenment, 1966.
[8] Tasks on thermodynamics and statistical physics. Ed. by P. Landsberg M.: World, 1974.
[9] A. M. Fedorchenko. Introduction to the course of statistical physics and thermodynamics. Kiev: Higher School, 1973.
[10] L. D. Landau, E. M. Lifshitz. Statistical physics. M.: Science, 1964.
[11] V. V. Shelest, D. A. Chervinskii, “Aspects of differential form calculus application in thermodynamics”, Vestnik Lugansk Vladimir Dahl National University, vol. 2 (4), part 1, pp.125-128, 2017.
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  • APA Style

    Valerii V. Shelest, Alexander V. Hristov, Dmitrii A. Chervinskii, Vladimir V. Rumyantsev. (2017). Thermodynamic Potentials Theory Aspects in External Differential Forms Calculus Representation. Journal of Photonic Materials and Technology, 3(2), 6-13. https://doi.org/10.11648/j.jmpt.20170302.11

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    ACS Style

    Valerii V. Shelest; Alexander V. Hristov; Dmitrii A. Chervinskii; Vladimir V. Rumyantsev. Thermodynamic Potentials Theory Aspects in External Differential Forms Calculus Representation. J. Photonic Mater. Technol. 2017, 3(2), 6-13. doi: 10.11648/j.jmpt.20170302.11

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    AMA Style

    Valerii V. Shelest, Alexander V. Hristov, Dmitrii A. Chervinskii, Vladimir V. Rumyantsev. Thermodynamic Potentials Theory Aspects in External Differential Forms Calculus Representation. J Photonic Mater Technol. 2017;3(2):6-13. doi: 10.11648/j.jmpt.20170302.11

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  • @article{10.11648/j.jmpt.20170302.11,
      author = {Valerii V. Shelest and Alexander V. Hristov and Dmitrii A. Chervinskii and Vladimir V. Rumyantsev},
      title = {Thermodynamic Potentials Theory Aspects in External Differential Forms Calculus Representation},
      journal = {Journal of Photonic Materials and Technology},
      volume = {3},
      number = {2},
      pages = {6-13},
      doi = {10.11648/j.jmpt.20170302.11},
      url = {https://doi.org/10.11648/j.jmpt.20170302.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.jmpt.20170302.11},
      abstract = {Thorough review of external differential forms calculus basic theses presented. Potentialities of this mathematical discipline, which can describe physical properties of dielectric materials, magnets and photonic materials influenced by mechanical, thermal and electromagnetic factors more logically and objectively, then traditional methods, demonstrated. Methodological effectiveness of the differential forms of thermodynamic potentials application in the macroscopic properties of homogeneous mono- and polyvariant systems description has been demonstrated. The simple, fundamental, symmetrical to the thermodynamic variables choice relations demonstrating the calculus of differential forms benefits have been obtained. Using Pfaffian forms thermodynamics, have been demonstrated, that differential forms calculus application to a description of the physical reality allows to operate physical concepts at a deeper level, based on the fundamental physical and mathematical principles.},
     year = {2017}
    }
    

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    T1  - Thermodynamic Potentials Theory Aspects in External Differential Forms Calculus Representation
    AU  - Valerii V. Shelest
    AU  - Alexander V. Hristov
    AU  - Dmitrii A. Chervinskii
    AU  - Vladimir V. Rumyantsev
    Y1  - 2017/07/27
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    N1  - https://doi.org/10.11648/j.jmpt.20170302.11
    DO  - 10.11648/j.jmpt.20170302.11
    T2  - Journal of Photonic Materials and Technology
    JF  - Journal of Photonic Materials and Technology
    JO  - Journal of Photonic Materials and Technology
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    UR  - https://doi.org/10.11648/j.jmpt.20170302.11
    AB  - Thorough review of external differential forms calculus basic theses presented. Potentialities of this mathematical discipline, which can describe physical properties of dielectric materials, magnets and photonic materials influenced by mechanical, thermal and electromagnetic factors more logically and objectively, then traditional methods, demonstrated. Methodological effectiveness of the differential forms of thermodynamic potentials application in the macroscopic properties of homogeneous mono- and polyvariant systems description has been demonstrated. The simple, fundamental, symmetrical to the thermodynamic variables choice relations demonstrating the calculus of differential forms benefits have been obtained. Using Pfaffian forms thermodynamics, have been demonstrated, that differential forms calculus application to a description of the physical reality allows to operate physical concepts at a deeper level, based on the fundamental physical and mathematical principles.
    VL  - 3
    IS  - 2
    ER  - 

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Author Information
  • Department of Theory of Complex Systems Dynamic Properties, Galkin Institute for Physics & Engineering, Donetsk, Ukraine

  • Department of Theory of Complex Systems Dynamic Properties, Galkin Institute for Physics & Engineering, Donetsk, Ukraine

  • Department of Theory of Complex Systems Dynamic Properties, Galkin Institute for Physics & Engineering, Donetsk, Ukraine

  • Department of Theory of Complex Systems Dynamic Properties, Galkin Institute for Physics & Engineering, Donetsk, Ukraine

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