Fundamental Principles of Statistical and Quantum Physics

  • Tian Ma
  • Shouhong Wang


This chapter is aimed for the first-principle approach to statistical physics and quantum physics, in the spirit of the guiding principles of physics: Principles  1.1.1 and  1.1.2. First, we introduce a new principle, the potential-descending principle (PDP), and show that statistical physics is built upon PDP and the principle of equal probability (PEP). Second, we develop a statistical theory of heat, including in particular the photon number formula of entropy, and the energy level formula of temperature. Also, we demonstrate that the physical carrier of heat is the photons. Third, we introduce a new field theoretical interpretation of quantum wave functions.


  1. Chaikin, P. M. and T. C. Lubensky (2000). Principles of condensed matter physics. Cambridge university press.Google Scholar
  2. de Gennes, P. (1966). Superconductivity of Metals and Alloys. W. A. Benjamin.zbMATHGoogle Scholar
  3. Fisher, M. E. (1998). Renormalization group theory: Its basis and formulation in statistical physics. Reviews of Modern Physics 70(2), 653.MathSciNetCrossRefGoogle Scholar
  4. Ginzburg, V. L. (2004). On superconductivity and superfluidity (what i have and have not managed to do), as well as on the ’physical minimum’ at the beginning of the xxi century. Phys.-Usp. 47, 1155–1170.CrossRefGoogle Scholar
  5. Gor’kov, L. (1968). Generalization of the Ginzburg-Landau equations for non-stationary problems in the case of alloys with paramagnetic impurities. Sov. Phys. JETP 27, 328–334.Google Scholar
  6. Kadanoff, L. P. (2000). Statistical physics: statics, dynamics and renormalization. World Scientific Publishing Co Inc.CrossRefGoogle Scholar
  7. Kleman, M. and O. D. Laverntovich (2007). Soft matter physics: an introduction. Springer Science & Business Media.Google Scholar
  8. Kosterlitz, J. M. and D. J. Thouless (1973). Ordering, metastability and phase transitions in two-dimensional systems. Journal of Physics C: Solid State Physics 6(7), 1181.CrossRefGoogle Scholar
  9. Landau, L. D. and E. M. Lifshitz (1969). Statistical Physics: V. 5: Course of Theoretical Physics. Pergamon press.Google Scholar
  10. Landau, L. D. and E. M. Lifshitz (1975). Course of theoretical physics, Vol. 2 (Fourth ed.). Oxford: Pergamon Press. The classical theory of fields, Translated from the Russian by Morton Hamermesh.Google Scholar
  11. Lifschitz, E. M. and L. P. Pitajewski (1990). Lehrbuch der theoretischen Physik (“Landau-Lifschitz”). Band X (Second ed.). Akademie-Verlag, Berlin. Physikalische Kinetik. [Physical kinetics], Translated from the Russian by Gerd Röpke and Thomas Frauenheim, Translation edited and with a foreword by Paul Ziesche and Gerhard Diener.Google Scholar
  12. Lifshitz, E. and L. Pitaevskii (1980). Statistical physics part 2, Landau and Lifshitz course of theoretical physics vol. 9.Google Scholar
  13. Liu, R., T. Ma, S. Wang, and J. Yang (2019). Thermodynamical potentials of classical and quantum systems. Discrete & Continuous Dynamical Systems - B; see also hal-01632278(2017) 24, 1411.Google Scholar
  14. Ma, T., R. Liu, and J. Yang (2018). Physical World from the Mathematical Point of View: Statistical Physics and Critical Phase Transition Theory (in Chinese). Science Press, Beijing.Google Scholar
  15. Ma, T. and S. Wang (2015a). Mathematical Principles of Theoretical Physics. Science Press, 524 pages.Google Scholar
  16. Ma, T. and S. Wang (2015c). Weakton model of elementary particles and decay mechanisms. Electronic Journal of Theoretical Physics, 139–178; see also Indiana University ISCAM Preprint 1304:
  17. Ma, T. and S. Wang (2016a). Quantum rule of angular momentum. AIMS Mathematics 1:2, 137–143.MathSciNetCrossRefGoogle Scholar
  18. Ma, T. and S. Wang (2016b). Spectral theory of differential operators and energy levels of subatomic particles. J. Math. Study 49, 259–292; see also Isaac Newton Institute Preprint NI14002:
  19. Ma, T. and S. Wang (2017a). Dynamic law of physical motion and potential-descending principle. J. Math. Study 50:3, 215–241; see also HAL preprint: hal--01558752.Google Scholar
  20. Ma, T. and S. Wang (2017d). Statistical theory of heat. Hal preprint: hal-01578634.Google Scholar
  21. Ma, T. and S. Wang (2017e). Topological Phase Transitions I: Quantum Phase Transitions. Hal preprint: hal-01651908.Google Scholar
  22. Ma, T. and S. Wang (2019). Quantum Mechanism of Condensation and High Tc Superconductivity. International Journal of Theoretical Physics B 33, 1950139 (34 pages); see also hal--01613117 (2017).Google Scholar
  23. Pathria, R. K. and P. D. Beale (2011). Statistical Mechanics (third ed.). Elsevier.zbMATHGoogle Scholar
  24. Pitaevskii, L. P. and S. Stringari (2016). Bose-Einstein condensation and superfluidity, Volume 164 of Internat. Ser. Mono. Phys. Oxford: Clarendon Press.CrossRefGoogle Scholar
  25. Reichl, L. E. (1998). A modern course in statistical physics (Second ed.). A Wiley-Interscience Publication. New York: John Wiley & Sons Inc.zbMATHGoogle Scholar
  26. Stanley, H. E. (1971). Introduction to Phase Transitions and Critical Phenomena. Oxford University Press, New York and Oxford.Google Scholar
  27. Tinkham, M. (1996). Introduction to Superconductivity. McGraw-Hill, Inc.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tian Ma
    • 1
  • Shouhong Wang
    • 2
  1. 1.Department of MathematicsSichuan UniversitySichuanChina
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA

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