A Primer for Deterministic Thermodynamics and Cryodynamics

Dedicated to the Founder of Synergetics Hermann Haken
  • Otto E. RosslerEmail author
  • Frank Kuske
  • Dieter Fröhlich
  • Hans H. Diebner
  • Thimo Böhl
  • Demetris T. Christopoulos
  • Christophe Letellier


The basic laws of deterministic many-body systems are summarized in the footsteps of the deterministic approach pioneered by Yakov Sinai . Two fundamental cases, repulsive and attractive, are distinguished. To facilitate comparison, long-range potentials are assumed both in the repulsive case and in the new attractive case. In Part I, thermodynamics —including the thermodynamics of irreversible processes along with chemical and biological evolution—is presented without paying special attention to the ad hoc constraint of long-range repulsion. In Part II, the recently established new fundamental discipline of cryodynamics, based on long-range attraction, is described in a parallel format. In Part III finally, the combination (“dilute hot-plasma dynamics”) is described as a composite third sister discipline with its still largely unknown properties. The latter include the prediction of a paradoxical “double-temperature equilibrium” or at least quasi-equilibrium existing, which has a promising technological application in the proposed interactive local control of hot-plasma fusion reactors. The discussion section puts everything into a larger perspective which even touches on cosmology.



We thank Yakov Sinai for his long-standing encouragement, and Ali Sanayei, Stefan C. Müller, Valerie Messager, Ralph Abraham, John Kozak, Daniel Stein, Jim Yorke, M.A. Aziz-Alaoui, Cyrille Bertelle, Werner Ebeling, Peter Plath, Boris Schapiro, Ramis Movassagh, Kenzei Hiwaki, George Lasker, Greg Andonian, Peter Weibel, Eric Klien, Andre Assis, Saurya Das, Günter Häfelinger, Alfred Rieckers, Wolfgang Müller-Schauenburg, Henry Gebhardt, Tobias Winkler, Niels Birbaumer, Walter Ratjen, Günter Radons, Luc Pastur, Dogwon Kim, Jürgen Parisi, Bill Seaman, Joachim Peinke, Rudolf Huebener, Stephen Wolfram, Leon Chua, Niels Schopohl and Matthias Bartelmann for discussions. For J.O.R.


  1. 1.
    O.E. Rossler, The new science of cryodynamics and its connection to cosmology. Complex Systems 20, 105–111 (2011)Google Scholar
  2. 2.
    L. Boltzmann, Lectures on Gas Theory, Translated by S.G. Brush (University of California Press, Berkeley, 1964)Google Scholar
  3. 3.
    Y. Sinai, Some remarks on the spectral properties of ergodic dynamical systems. Russ. Math. Surv. 5, 37–50 (1963)CrossRefzbMATHGoogle Scholar
  4. 4.
    Y. Sinai, Dynamical systems with elastic reflections. Russ. Math. Surv. 25, 137–189 (1970)Google Scholar
  5. 5.
    A. Kolmogorov, On conservation of conditionally periodic motions for a small change in Hamilton’s function (O sohranenii uslovnoperiodicheskhi dvizhenij pri malom izmenenii funkcii Gamil’tona), Dokl. Akad. Nauk. SSSR 98, 527–530 (1954); V.I. Arnold, Proof of a theorem of A.N. Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian. Russian Mathematical Surveys 18:5, 9–36 (1963); J. Moser, On invariant curves of area-preserving mappings of an annulus. Nachr. Akad. Wiss. Gött. Math. Phys. Kl, 1–20 (1962)Google Scholar
  6. 6.
    R. Clausius, On several convenient forms of the fundamental equations of the mechanical theory of heat (Über verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie). Ann. Phys. Chem. 125, 352–400 (1865)Google Scholar
  7. 7.
    J. Gibbs, Elementary Principles in Statistical Mechanics, Developed with Especial Reference to the Rational Foundation of Thermodynamics (Yale University Press, New Haven, 1902), republished by Dover in 1960Google Scholar
  8. 8.
    H. Diebner, O.E. Rossler, A deterministic entropy based on the instantaneous phase space volume. Z. Naturforsch. 53a, 51–60 (1998)Google Scholar
  9. 9.
    K. Sonnleitner, StV4: A symplectic time-reversible Störmer-Verlet algorithm of fourth order for Hamiltonian several-particle systems including two applied examples—gas and T-tube arrangement (StV4: Ein symplektisches zeitreversibles Störmer-Verlet-Verfahren vierter Ordnung für Hamiltonsche Mehrteilchensysteme mit zwei Anwendungsbeispielen (Gas, T-Rohr-Anordnung), (Ph.D. thesis, University of Tübingen 2010)Google Scholar
  10. 10.
    F. Brando, M. Horodecki, N. Ng, J. Oppenheim, S. Wehner, The second laws of quantum thermodynamics. Proc. Natl. Acad. Sci. USA 112, 3275–3279 (2015). CrossRefGoogle Scholar
  11. 11.
    O.E. Rossler, An estimate of Planck’s constant, in Dynamic Phenomena in Neurochemistry and Neurophysics: Theoretical Aspects (Publications of the Hungarian Academy of Sciences, Budapest, 1985), pp. 16–18Google Scholar
  12. 12.
    L. Bertalanffy, Theoretical Biology (Theoretische Biologie I) (Gebrüder Bornträger, Berlin, 1932)Google Scholar
  13. 13.
    I. Prigogine, Dissipative structures in chemical systems, in Fast Reactions and Primary Processes in Chemical Kinetics, ed. by S. Claesson (Interscience, New York, 1967); I. Prigogine, W. Kestemont and M. Marechal, Velocity correlation and irreversibility: a molecular-dynamics approach, in From Chemical to Biological Organization, ed. by M. Markus, S.C. Müller, G. Nicolis (Springer, New York, 1988), pp. 22–26Google Scholar
  14. 14.
    O.E. Rossler, A system-theoretic model of biogenesis. Z. Naturforsch. 26b, 741–746 (1971)Google Scholar
  15. 15.
    O.E. Rossler, Deductive prebiology, in Molecular Evolution and Prebiology, ed. by K. Matsuno (Plenum Press, New York 1984), pp. 375–385. 27
  16. 16.
    O.E. Rossler, Is benevolence compatible with intelligence—on the theory of the humane feeling (in German), in The Theme Park of the Expo 2000, vol. 1: Planet of Visions, Knowledge, Information, Communication (Springer, Vienna, 2000), pp. 157–163Google Scholar
  17. 17.
    P. Teilhard de Chardin, The Future of Man (Harper and Row, New York, 1964)Google Scholar
  18. 18.
    R. Forward, Dragon’s Egg (Del Rey, New York, 1980)Google Scholar
  19. 19.
    H. Follmann, C. Brownson, Darwin’s warm little pond revisited: from molecules to the origin of life. Naturwissenschaften 96, 1265–1292 (2009). CrossRefGoogle Scholar
  20. 20.
    E. Schrödinger, What Is Life? The Physical Aspect of the Living Cell (Cambridge University Press, 1944)Google Scholar
  21. 21.
    J. van der Waals, On the Continuity of the Gaseous and Liquid States (in Dutch), Ph.D, thesis, Leiden University, 1873Google Scholar
  22. 22.
    A. Aranda, J.A. Lopez, C.O. Dorso, V. Furci, Mapping the phase diagram of nuclear matter. Bull. Can.-Am.-Mex. Phys. Soc. (1987)Google Scholar
  23. 23.
    W. Nernst, Über die Berechnung chemischer Gleichgewichte aus thermischen Messungen (On Calculating Chemical Equilibria from Thermal Measurements), (Nachr. Kgl. Ges. Wiss. Göttingen, 1906), pp. 1–40Google Scholar
  24. 24.
    H. Kammerlingh-Onnes, Further experiments with liquid Helium, D. On the change of electric resistance of pure metals at very low temperatures, etc., V. The disappearance of the resistance of Mercury, Comm. Phys. Lab. Univ. Leiden, 122b (1911)Google Scholar
  25. 25.
    P. Kapitza, Viscosity of liquid Helium below the Lambda Point. Nature 141, 74 (1938)CrossRefGoogle Scholar
  26. 26.
    J. Bardeen, Theory of non-Ohmic conduction from charge-density waves in NbSe3. Phys. Rev. Lett. 42, 1498–1500 (1979). CrossRefGoogle Scholar
  27. 27.
    S. Bose, Planck‘s law and light-quantum hypothesis (in German). Zeitschrift für Physik 26, 178–181 (1924). CrossRefGoogle Scholar
  28. 28.
    K.V. Klitzing, G. Dorda, M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45, 494–497 (1980).
  29. 29.
    R.B. Laughlin, Anomalous Quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395–1398 (1983). CrossRefGoogle Scholar
  30. 30.
    S. Braun, J.P. Ronzheimer, M. Schreiber, S.S. Hodgman, T. Rom, I. Bloch, U. Schneider, Negative absolute temperature for motional degrees of freedom. Science 339, 52–55 (2013). CrossRefGoogle Scholar
  31. 31.
    S. Chandrasekhar, Dynamical friction, I. General considerations: the coefficient of dynamical friction, Astrophys. J. 97, 255–262 (1943).
  32. 32.
    P. Schneider, Extragalactic Astronomy and Cosmology (Springer, Heidelberg, 2015), p. 119Google Scholar
  33. 33.
    O.E. Rossler, F. Kuske and A. Sanayei, Deterministic antidissipation. in Bottom-up Self-Organization in Supramolecular Soft Matter, ed. by S.C. Müller, J. Parisi (Springer, Berlin, 2015), pp. 271–280Google Scholar
  34. 34.
    CERN 2008, LSAG report, review of the safety of LHC collisions,
  35. 35.
    L.D. Landau, On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. Physikalische Zeitschrift Sowjetunion 1, 285–288 (1932)Google Scholar
  36. 36.
    D. Lynden-Bell, Stellar dynamics: Exact solution of the self-gravitation equation. Mon. Not. R. Astron. Soc. 123, 447–458 (1961). CrossRefzbMATHMathSciNetGoogle Scholar
  37. 37.
    J. Binney and S. Tremaine, Galactic Dynamics (Princeton University Press, Princeton, 2008), p. 547Google Scholar
  38. 38.
    M. Hotinceanu, Z. Borsos, O. Dinu, Aspects of thermodynamic equilibrium in plasma. Pet. Gas Univ. Ploiesti Bull. 62, 97–102 (2010)Google Scholar
  39. 39.
    O.E. Rossler, F. Kuske, A. Sanayei, Cryodynamics can solve the energy problem by stabilizing ITER: a prediction, in Numerical Analysis and Applied Mathematics ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics (AIP Publishing, Melville, 2012), pp. 642–645.; O.E. Rossler, Hamiltonian chaos: two-temperature equilibrium in hot plasmas predicted, in Fourth International Conference on Complex Systems and Applications ICCSA 2014, pp. 24–27
  40. 40.
    P. Seeliger, Perspective contributions of atomic and nuclear processes to a carbon-free energy economy of the future (in German). Sitzungsberichte der Leibniz-Sozietät der Wissenschaften zu Berlin 130, 165–187 (2017), cf. p. 171Google Scholar
  41. 41.
    O.E. Rossler, A. Sanayei, Is hot fusion made feasible by the discovery of cryodynamics? in Nostradamus: Modern Methods of Prediction, Modeling and Analysis of Nonlinear Systems (Springer, Berlin, 2013), pp. 1–4Google Scholar
  42. 42.
    C.S. Adams, H.J. Lee, N. Davidson, M. Kasevich, S. Chu, Evaporative cooling in a crossed dipole trap. Phys. Rev. Lett. 74, 3577–3580 (1995). CrossRefGoogle Scholar
  43. 43.
    T. McGuire, The lockheed Martin compact fusion reactor. Thursday Colloquium, Princeton University, August 6, 2015Google Scholar
  44. 44.
    G. Farmelo, The Strangest Man—The Hidden Life of Paul Dirac, Quantum Genius (Faber and Faber, London, 2009)zbMATHGoogle Scholar
  45. 45.
    J.J. Waterston, On the physics of media that are composed of free and perfectly elastic molecules in a state of motion (1845). Philos. T. R. Soc. Lond. A 183, 1–79 (1892), (edited after 47 years by Lord Rayleigh).
  46. 46.
    J. van Helmont, Oriatrike or Physick Refined (Lodowick Loyd, London, 1662)Google Scholar
  47. 47.
    H. Diebner, Time-dependent deterministic entropies and dissipative structures in exactly reversible Newtonian molecular-dynamics universes (in German) (Grauer-Verlag, Stuttgert 1999). Ph.D. Thesis, University of TübingenGoogle Scholar
  48. 48.
    R. Descartes, Principles of Philosophy (Latin original 1644) (Kluwer, Dordrecht, 1991)Google Scholar
  49. 49.
    H. Poincare, On the three-body problem and the equations of dynamics (in French). Acta Math. 13, 1–270 (1890), cf. J. Barrow-Green, Poincaré and the Three-Body Problem, Vol. 2 (American Mathematical Society. Providence, R.I., 1997)Google Scholar
  50. 50.
    R. Movassagh, A time-asymmetric process in central force scatterings (2013), arXiv:1008.0875[physics.class-ph]
  51. 51.
    O.E. Rossler, R. Movassagh, Bitemporal Sinai divergence: an energetic analog to Boltzmann’s entropy? Int. J. Nonlin. Sci. Num. 6, 349–350 (2005)CrossRefGoogle Scholar
  52. 52.
    E. Fournier d’Albe, Two new Worlds (I) The Infra-World, (II) The Supra World (World and Longman Green, Longmans, Green and Co., London 1907)Google Scholar
  53. 53.
    B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1977)Google Scholar
  54. 54.
    P.H. Coleman, L. Pietronero, The fractal nature of the universe. Phys. A 185, 45–55 (1992). CrossRefGoogle Scholar
  55. 55.
    V.C. Rubin, N. Thonnard, W.K. Ford, Jr., Extended rotation curves of high-luminosity spiral galaxies, IV: Systematic dynamical properties SA through SC. Astrophys. J. 225, L 101–111 (1978).
  56. 56.
    R. Giacconi, et al., The Chandra Deep field south one million seconds catalog. Astrophys. J. Suppl. 139, 369–410 (2002)Google Scholar
  57. 57.
    F. Zwicky, On the red shift of spectral lines through interstellar space. Proc. Natl. Acad. Sci. USA 15, 773–779 (1929)CrossRefzbMATHGoogle Scholar
  58. 58.
    O.E. Rossler, The c-global revival in physics. Prog. Phys. 11, 340–343 (2015)Google Scholar
  59. 59.
    S. Mason, A History of the Sciences (Collier-MacMillan, New York, 1968)Google Scholar
  60. 60.
    S. Sambursky, Physical World of Late Antiquity (Basic Books, New York, 1962)Google Scholar
  61. 61.
    A. Assis, M. Newes, History of the 2.7 K temperature prior to Penzias and Wilson. Apeiron 2, 79–84 (1995)Google Scholar
  62. 62.
    M. Scheler, Man’s Place in Nature (Noonday, New York, 1961)Google Scholar
  63. 63.
    A. Sanayei, O. Rossler, Chaotic Harmony—A Dialog about Physics, Complexity and Life (Springer, Heidelberg, 2014)zbMATHGoogle Scholar
  64. 64.
    O.E. Rossler, Rolling ball in breathing plane-tree alley paradigm. Eur. Sci. J. 9, 1–7 (2013)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Otto E. Rossler
    • 1
    Email author
  • Frank Kuske
    • 1
  • Dieter Fröhlich
    • 1
  • Hans H. Diebner
    • 2
  • Thimo Böhl
    • 1
  • Demetris T. Christopoulos
    • 3
  • Christophe Letellier
    • 4
  1. 1.Division of Theoretical ChemistryUniversity of TübingenTübingenGermany
  2. 2.Department of Medical InformationTechnical University DresdenDresdenGermany
  3. 3.Department of EconomicsNational and Kapodistrian University of AthensAthensGreece
  4. 4.Physics DepartmentUniversity of Rouen CORIASaint-Étienne du RouvrayFrance

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