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Some Implications of a Scale Invariant Model of Statistical Mechanics to Classical and Relativistic Thermodynamics

Year 2014, , 233 - 248, 31.03.2014
https://doi.org/10.5541/ijot.585

Abstract

Some implications of a scale invariant model of statistical mechanics to the mechanical theory of heat of Helmholtz and Clausius are described. Modified invariant definitions of heat and entropy are presented closing the gap between radiation and gas theory. Modified relativistic transformations of pressure, Boltzmann constant, entropy, and density are introduced leading to transformation of ideal gas law. Following Helmholtz the total thermal energy of thermodynamic system is decomposed into free heat U and latent heat p V and identified as modified form of the first law of thermodynamics Q = H = U + p V. Subjective versus objective aspects of Boltzmann thermodynamic entropy versus Shannon information entropy are discussed. Also, modified thermodynamic properties of ideal gas are presented. The relativistic thermodynamics being described is in accordance with Poincaré - Lorentz dynamic theory of relativity as opposed to Einstein kinematic theory of relativity since the former theory that is based on compressible ether of Planck is causal as was emphasized by Pauli.

References

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  • L. de Broglie, Non-Linear Wave Mechanics: A Causal Interpretation, Elsevier, New York,1960.
  • L. de Broglie, The Reinterpretation of Wave Mechanics. Found. Phys. 1, 5-15, 1970.
  • E. Madelung, “Quantentheorie in Hydrodynamischer Form,” Z. Physik. 40, 332-326, 1926.
  • E. Schrödinger, Über die Umkehrung der Naturgesetze , Sitzber Preuss Akad Wiss Phys -Math Kl, 144-153 , 19 R. Fürth, Über Einige Beziehungen zwischen klassischer Staristik und Quantenmechanik,  . Phys. 81, 143-162, 1933.
  • D. Bohm, A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables. I, Phys. Rev. 85, 166-179, 1952.
  • T. Takabayasi, On the Foundation of Quantum Mechanics Associated with Classical Pictures, Prog. Theor. Phys. 8, 143-182, 1952.
  • D., Bohm, and J. P. Vigier, Model of the Causal Interpretation of Quantum Theory in Terms of a Fluid with Irregular Fluctuations, Phys. Rev. 96, 208-217, 19 E. Nelson, Derivation of the Schrödinger Equation from Newtonian Mechanics. Phys. Rev. 150, 10791085, 1966.
  • E. Nelson, Quantum Fluctuations, Princeton University Press, Princeton, New Jersey, 1985.
  • L. de la Peña, New Foundation of Stochastic Theory of Quantum Mechanics. J. Math. Phys. 10, 1620-1630, 19
  • L. de la Peña, and A. M. Cetto, Does Quantum Mechanics Accept a Stochastic Support? Found. Phys. 12,1017-1037, 1982.
  • A. O. Barut, Schrödinger’s Interpretation of  as a Continuous Charge Distribution. Ann. der Phys. 7, 3136, 1988.
  • A. O. Barut, and A. J. Bracken, Zitterbewegung and the Internal Geometry of the Electron. Phys. Rev. D 23, 2454-2463, 1981.
  • J. P. Vigier, De Broglie Waves on Dirac Aether: A Testable Experimental Assumption, Lett. Nuvo Cim. 29, 467-475, 1980; Ph. Gueret, and J. P. Vigier, De Broglie’s Wave Particle Duality in the Stochastic Interpretation of Quantum Mechanics: A Testable Physical Assumption, Found. Phys. 12, 1057-1083, 1982; C. Cufaro Petroni, and J. P. Vigier, Dirac’s Aether in Relativistic Quantum Mechanics, Found. Phys. 13, 253-286, 1983; J. P. Vigier, Derivation of Inertia Forces from the Einstein-de Broglie-Bohm (E.d.B.B) Causal Stochastic Interpretation of Quantum Mechanics, Found. Phys. 25, 1461-1494, 1995.
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  • T. Kármán, and L. Howarth, On the Statistical Theory of Isotropic Turbulence, Proc. Roy. Soc. A 164, 192215, 1938.
  • H. P. Robertson, The Invariant Theory of Isotropic Turbulence, Proc. Camb. Phil. Soc. 36, 209-223 1940.
  • A. N. Kolmogoroff, Local Structure on Turbulence in Incompressible Fluid, C. R. Acad. Sci. U. R. S. S. 30, 301-305, 1941; Dissipation of Energy in Locally Isotropic Turbulence, C. R. Acad. Sci. U. R. S. S. 32, 1921, 1942; A Refinement of Previous Hypothesis Concerning the Local Structure of Turbulence in a Viscous Incompressible Fluid at High Reynolds Number, J. Fluid Mech. 13, 82-85, 1962.
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  • H. Tennekes, and J. L. Lumley, A First Course In Turbulence, MIT Press, 1972.
  • S. H. Sohrab, “Transport Phenomena and Conservation Equations in Multicomponent Chemically-Reactive Ideal Gas Mixtures,” Proceeding of the 31st ASME National Heat Transfer Conference, HTD-Vol. 328, 1996, pp. 37-60.
  • S. H. Sohrab, A Scale Invariant Model of Statistical Mechanics and Modified Forms of the First and the Second Laws of Thermodynamics, Rev. Gén. Therm. 38, 845-853, 1999.
  • S. H. Sohrab, “The Nature of Mass, Dark Matter, and Dark Energy in Cosmology and the Foundation of Relativistic Thermodynamics,” In: New Aspects of Heat Transfer, Thermal Engineering, and Environment. S. H. Sohrab, H. J. Catrakis, N. Kobasko, (Eds.), WSEAS Press, 2008, pp. 434-442.
  • S. H. Sohrab, Boltzmann Entropy of Thermodynamics versus Shannon Entropy of Information Theory. Int. J. Mech. 8, 73-84, 2014.
  • S. H. Sohrab, Invariant Planck Energy Distribution Law and its Connection to the Maxwell-Boltzmann Distribution Function. WSEAS Transactions on Mathematics 6, 254-262, 2007.
  • S. H. Sohrab, “Derivation of Invariant Forms of Conservation Equations from the Invariant Boltzmann Equation,” In: Theoretical and Experimental Aspects of Fluid Mechanics, S. H. Sohrab, H. C. Catrakis, and F. K. Benra (Eds.),WSEAS Press, 2008, pp. 27-35.
  • S. H. Sohrab, “Universality of a Scale Invariant model of Turbulence and its Quantum Mechanical Foundation,” In: Recent Advances in Fluid Mechanics & Aerodynamics, S. Sohrab, H. Catrakis, and. N. Kobasko (Eds.), WSEAS Press, 2009, pp. 134-140.
  • S. H. Sohrab, “On a scale invariant model of statistical mechanics and derivation of invariant forms of conservation equations from invariant Boltzmann and Enskog equations,”. Proceedings of The 2014 International Conference on Mechanics, Fluid Mechanics, Heat and Mass Transfer, February 22-24, Interlaken, Switzerland, 2014, pp. 19-37.
  • S. H. Sohrab, “Some implications of a scale invariant model of statistical mechanics to classical and relativistic thermodynamics,”. In: Recent Researches in Electric and Energy Systems, Ki Young Kim, Dario Assante, Marian Ciontu, and Jana Jirickova (Eds.), WSEAS press, Athens, 2013, pp. 298-313.
  • G. ‘t Hooft, Quantum Gravity as a Dissipative Deterministic System, Class. Quantum Grav. 16, 32633279, 1999.
  • R. Clausius, Ueber einen auf die Wärme anwendbaren mechanischen Satz. Sitzungsberichte der Niedderrheinischen Gesellschaft, Bonn, 114-119, 1870.
  • S. H. Sohrab, Scale-Invariant Form of the Planck Law of Energy Distribution and its Connection to the Maxwell-Boltzmann Distribution, Bull. Amer. Phys. Soc. 49, 255, 2004.
  • S. Chandrasekhar, Newton’s Principia for the Common Reader, 579-593, Oxford University Press, New York, 19 G. S. Brush, Kinetic Theory, Vol.1-3, Pergamon Press, New York, 1965.
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  • W. Pauli, Pauli Lectures on Physics, Vol.3, p. 14, MIT Press, 1973.
  • C. A. Long, and S. H. Sohrab, “The Power of Two, Speed of Light, Force and Energy and the Universal Gas Constant,”. In: Recent Advances on Applied Mathematics, C. A. Long, S. H. Sohrab, G. Bognar, and L. Perlovsky, (Eds.), WSEAS Press, 2008, pp. 434-442.
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  • F. Hasenöhrl, Zur Theorie der Strahlung in bewegten Körpern. Ann. der Physik 15, 344-370, 1905. Zur Theorie der Strahlung in bewegten Körpern. Ann. der Phys. 16, 589-592, 1905.
  • A. Einstein, Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? Ann. der Phys. (Leipzig) 18, 639-641, 1905.
  • M. Kardar, Statistical Physics of Particles, Cambridge University Press, New York, 2007.
  • R. E. Sonntag, and G. E. van Wylen, Fundamentals of Statistical Thermodynamics, Wiley, New York, 1966.
  • W. Yourgrau, A. van der Merwe, and G. Raw, Treatise on Irreversible and Statistical Thermodynamics, Dover, New York, 1982.
  • C. E. Shannon, The Mathematical Theory of Communication, Bell System Tech. J. 27, 379-423 and 623-656, 1948.
  • W. Weaver, and C. E. Shannon, The Mathematical Theory of Communication, University of Illinois Press, Chicago, 1963. L. Boltzmann, Weitere Studien uber das Warmegleichgewicht unter Gasmoleculen. Sitzungsberichte Akad.Wiss., Vienna, Part II, 66¸ 275370, 1872. English translation in: G. S. Brush, Kinetic Theory, Vol.1-3, pp. 88-175, Pergamon Press, New York, 1965.
  • L. Boltzmann, Lectures on Gas Theory, Dover, New York, 1964.
  • O. Darrigol, Statistics and Combinatorics in Early Quantum Theory, Historical Studies in the Physical and Biological Sciences,19, 17-80, 1988; Statistics and Combinatorics in Early Quantum Theory, II: Early Symptoms of Indistinguishability and Holism, 21, 237298, 1991.
  • L. Brillouin, Maxwell Demon Cannot Operate: Information and Entropy I, J. Appl. Phys. 22, 334-337, 19 A. Ben-Naim, Entropy Demystified, World Scientific, New York, 2008.
  • M. Planck, Where Is Science Going, Ox Bow Press, Connecticut, 1981.
  • A. Ben-Naim, A Farewell to Entropy: Statistical Thermodynamics Based on Information, World Scientific, New York, 2008.
  • M. Planck, Zur Dynamik bewegter Systeme, Sitzungsber. Preuss. Akad. Wiss., 542; Ann. Physik 26, 1, 190 K. Mosengeil, Theorie der stationären Strahlung in einem gleichförmig bewegten Hohlraum, Ann. Physik 22, 876, 1907.
  • A. Einstein, Relativitätsprinzip und die aus demselben gezogenen Folgerungen, Jahrb. Radioaktivität und Elektron 5, 411, 1907. M. Laue, Das Relativitätsprinzip . Friedr. Vieweg & Sohn, Braunschweig , 19
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  • W. Pauli, Theory of Relativity, p.135, Dover, 1958.
  • H. Poincaré, Sur la Dynamique de l’Electron, C. R. Acad. Sci. Paris 140, 1504-1508, 1905.
  • H. Poincaré, Sur la Dynamique de l’Electron, Rend. Circ. Mat. Palermo 21, 9-175, 1906.
  • A. Einstein, Zur Elecrodynamik bewegter Körper, Ann. der Phys. (Leipzig) 17, 891-921, 1905.
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  • W. Schroeder, and H-J. Treder, The "Einstein-Laue" discussion. BJHS 27, 1113, 1992.
  • P. T. Landsberg, and G. E. A. Matsas, Laying the Ghost of the Relativistic Temperature Transformation, Phys. Lett. A. 23, 401, 1996.
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Year 2014, , 233 - 248, 31.03.2014
https://doi.org/10.5541/ijot.585

Abstract

References

  • L. de Broglie, Interference and Corpuscular Light. Nature 118, 2969, 441-442, 1926; Sur la Possibilité de Relier les Phénomènes d'Interférence et de Diffraction à la Théorie des Quanta de Lumière. C. R. Acad. Sci. Paris, 183, 447-448, 1927; La Structure Atomique de la Matière et du Rayonnement et la Mécanique Ondulatoire. 184, 273-274, 1927; Sur le Rôle des Ondes Continues en Mécanique Ondulatoire. 185, 380-382, 19
  • L. de Broglie, Non-Linear Wave Mechanics: A Causal Interpretation, Elsevier, New York,1960.
  • L. de Broglie, The Reinterpretation of Wave Mechanics. Found. Phys. 1, 5-15, 1970.
  • E. Madelung, “Quantentheorie in Hydrodynamischer Form,” Z. Physik. 40, 332-326, 1926.
  • E. Schrödinger, Über die Umkehrung der Naturgesetze , Sitzber Preuss Akad Wiss Phys -Math Kl, 144-153 , 19 R. Fürth, Über Einige Beziehungen zwischen klassischer Staristik und Quantenmechanik,  . Phys. 81, 143-162, 1933.
  • D. Bohm, A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables. I, Phys. Rev. 85, 166-179, 1952.
  • T. Takabayasi, On the Foundation of Quantum Mechanics Associated with Classical Pictures, Prog. Theor. Phys. 8, 143-182, 1952.
  • D., Bohm, and J. P. Vigier, Model of the Causal Interpretation of Quantum Theory in Terms of a Fluid with Irregular Fluctuations, Phys. Rev. 96, 208-217, 19 E. Nelson, Derivation of the Schrödinger Equation from Newtonian Mechanics. Phys. Rev. 150, 10791085, 1966.
  • E. Nelson, Quantum Fluctuations, Princeton University Press, Princeton, New Jersey, 1985.
  • L. de la Peña, New Foundation of Stochastic Theory of Quantum Mechanics. J. Math. Phys. 10, 1620-1630, 19
  • L. de la Peña, and A. M. Cetto, Does Quantum Mechanics Accept a Stochastic Support? Found. Phys. 12,1017-1037, 1982.
  • A. O. Barut, Schrödinger’s Interpretation of  as a Continuous Charge Distribution. Ann. der Phys. 7, 3136, 1988.
  • A. O. Barut, and A. J. Bracken, Zitterbewegung and the Internal Geometry of the Electron. Phys. Rev. D 23, 2454-2463, 1981.
  • J. P. Vigier, De Broglie Waves on Dirac Aether: A Testable Experimental Assumption, Lett. Nuvo Cim. 29, 467-475, 1980; Ph. Gueret, and J. P. Vigier, De Broglie’s Wave Particle Duality in the Stochastic Interpretation of Quantum Mechanics: A Testable Physical Assumption, Found. Phys. 12, 1057-1083, 1982; C. Cufaro Petroni, and J. P. Vigier, Dirac’s Aether in Relativistic Quantum Mechanics, Found. Phys. 13, 253-286, 1983; J. P. Vigier, Derivation of Inertia Forces from the Einstein-de Broglie-Bohm (E.d.B.B) Causal Stochastic Interpretation of Quantum Mechanics, Found. Phys. 25, 1461-1494, 1995.
  • F. T. Arecchi, and R. G. Harrison, Instabilities and Chaos in Quantum Optics, Springer-Verlag, Berlin, 19 O. Reynolds, On the Dynamical Theory of Incompressible Viscous Fluid and the Determination of the Criterion, Phil. Trans. Roy. Soc. A 186, 23-164, 18 D. Enskog, Kinetische Theorie der Vorgange in Massig Verdunnten Gasen, by Almqvist and Wiksells Boktryckeri-A.B., Uppsala, 1917. English translation in Ref. [63], pp.125-225.
  • G. I. Taylor, Statistical Theory of Turbulence-Parts IIV. Proc. Roy. Soc. A 151, 421-478, 1935.
  • T. Kármán, and L. Howarth, On the Statistical Theory of Isotropic Turbulence, Proc. Roy. Soc. A 164, 192215, 1938.
  • H. P. Robertson, The Invariant Theory of Isotropic Turbulence, Proc. Camb. Phil. Soc. 36, 209-223 1940.
  • A. N. Kolmogoroff, Local Structure on Turbulence in Incompressible Fluid, C. R. Acad. Sci. U. R. S. S. 30, 301-305, 1941; Dissipation of Energy in Locally Isotropic Turbulence, C. R. Acad. Sci. U. R. S. S. 32, 1921, 1942; A Refinement of Previous Hypothesis Concerning the Local Structure of Turbulence in a Viscous Incompressible Fluid at High Reynolds Number, J. Fluid Mech. 13, 82-85, 1962.
  • A. M. Obukhov, On the Distribution of Energy in the Spectrum of Turbulent Flow, C. R. Acad. Sci. U. R. S. S. 32, 19-22, 1941; Some Specific Features of Atmospheric Turbulence, J. Fluid Mech. 13, 77-81, 19
  • S. Chandrasekhar, Stochastic Problems in Physics and Astronomy, Rev. Mod. Phys. 15, 1-89, 1943.
  • S. Chandrasekhar, Stochastic, Statistical, and Hydrodynamic Problems in Physics and Astronomy, Selected Papers, vol.3, University of Chicago Press, Chicago, 1989, pp. 199-206.
  • W. Heisenberg, On the Theory of Statistical and Isotropic Turbulence, Proc. Roy. Soc. A 195, 402-406, 1948; Zur Statistischen Theorie der Turbulenz, Z. Phys. 124, 628-657, 1948.
  • G. K. Batchelor, The Theory of Homogeneous Turbulence, Cambridge University Press, Cambridge, 19 L. D. Landau, and E. M. Lifshitz, Fluid Dynamics, Pergamon Press, New York, 1959.
  • H. Tennekes, and J. L. Lumley, A First Course In Turbulence, MIT Press, 1972.
  • S. H. Sohrab, “Transport Phenomena and Conservation Equations in Multicomponent Chemically-Reactive Ideal Gas Mixtures,” Proceeding of the 31st ASME National Heat Transfer Conference, HTD-Vol. 328, 1996, pp. 37-60.
  • S. H. Sohrab, A Scale Invariant Model of Statistical Mechanics and Modified Forms of the First and the Second Laws of Thermodynamics, Rev. Gén. Therm. 38, 845-853, 1999.
  • S. H. Sohrab, “The Nature of Mass, Dark Matter, and Dark Energy in Cosmology and the Foundation of Relativistic Thermodynamics,” In: New Aspects of Heat Transfer, Thermal Engineering, and Environment. S. H. Sohrab, H. J. Catrakis, N. Kobasko, (Eds.), WSEAS Press, 2008, pp. 434-442.
  • S. H. Sohrab, Boltzmann Entropy of Thermodynamics versus Shannon Entropy of Information Theory. Int. J. Mech. 8, 73-84, 2014.
  • S. H. Sohrab, Invariant Planck Energy Distribution Law and its Connection to the Maxwell-Boltzmann Distribution Function. WSEAS Transactions on Mathematics 6, 254-262, 2007.
  • S. H. Sohrab, “Derivation of Invariant Forms of Conservation Equations from the Invariant Boltzmann Equation,” In: Theoretical and Experimental Aspects of Fluid Mechanics, S. H. Sohrab, H. C. Catrakis, and F. K. Benra (Eds.),WSEAS Press, 2008, pp. 27-35.
  • S. H. Sohrab, “Universality of a Scale Invariant model of Turbulence and its Quantum Mechanical Foundation,” In: Recent Advances in Fluid Mechanics & Aerodynamics, S. Sohrab, H. Catrakis, and. N. Kobasko (Eds.), WSEAS Press, 2009, pp. 134-140.
  • S. H. Sohrab, “On a scale invariant model of statistical mechanics and derivation of invariant forms of conservation equations from invariant Boltzmann and Enskog equations,”. Proceedings of The 2014 International Conference on Mechanics, Fluid Mechanics, Heat and Mass Transfer, February 22-24, Interlaken, Switzerland, 2014, pp. 19-37.
  • S. H. Sohrab, “Some implications of a scale invariant model of statistical mechanics to classical and relativistic thermodynamics,”. In: Recent Researches in Electric and Energy Systems, Ki Young Kim, Dario Assante, Marian Ciontu, and Jana Jirickova (Eds.), WSEAS press, Athens, 2013, pp. 298-313.
  • G. ‘t Hooft, Quantum Gravity as a Dissipative Deterministic System, Class. Quantum Grav. 16, 32633279, 1999.
  • R. Clausius, Ueber einen auf die Wärme anwendbaren mechanischen Satz. Sitzungsberichte der Niedderrheinischen Gesellschaft, Bonn, 114-119, 1870.
  • S. H. Sohrab, Scale-Invariant Form of the Planck Law of Energy Distribution and its Connection to the Maxwell-Boltzmann Distribution, Bull. Amer. Phys. Soc. 49, 255, 2004.
  • S. Chandrasekhar, Newton’s Principia for the Common Reader, 579-593, Oxford University Press, New York, 19 G. S. Brush, Kinetic Theory, Vol.1-3, Pergamon Press, New York, 1965.
  • H. Helmholtz, Über der Ehaltung der Kraft, Eine Physikalische Abhandlung. G. Reiner, Berlin, 1947. English translation in: G. S. Brush, Kinetic Theory, Vol.1-3, Pergamon Press, New York, 1965.
  • W. Pauli, Pauli Lectures on Physics, Vol.3, p. 14, MIT Press, 1973.
  • C. A. Long, and S. H. Sohrab, “The Power of Two, Speed of Light, Force and Energy and the Universal Gas Constant,”. In: Recent Advances on Applied Mathematics, C. A. Long, S. H. Sohrab, G. Bognar, and L. Perlovsky, (Eds.), WSEAS Press, 2008, pp. 434-442.
  • O. De Pretto, Ipotesi dell’Etere Nella Vita dell’Universo, Reale, Inst. Veneto di Scienze, Lettere en Arti 63, 439-500, 1904.
  • H. Poincaré, La Théorie de Lorentz et le Principe de Réaction. Arch. Neerland. 5, 252-278, 1900; http://www.physicsinsights.org/poincare-1900.pdf.
  • F. Hasenöhrl, Zur Theorie der Strahlung in bewegten Körpern. Ann. der Physik 15, 344-370, 1905. Zur Theorie der Strahlung in bewegten Körpern. Ann. der Phys. 16, 589-592, 1905.
  • A. Einstein, Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? Ann. der Phys. (Leipzig) 18, 639-641, 1905.
  • M. Kardar, Statistical Physics of Particles, Cambridge University Press, New York, 2007.
  • R. E. Sonntag, and G. E. van Wylen, Fundamentals of Statistical Thermodynamics, Wiley, New York, 1966.
  • W. Yourgrau, A. van der Merwe, and G. Raw, Treatise on Irreversible and Statistical Thermodynamics, Dover, New York, 1982.
  • C. E. Shannon, The Mathematical Theory of Communication, Bell System Tech. J. 27, 379-423 and 623-656, 1948.
  • W. Weaver, and C. E. Shannon, The Mathematical Theory of Communication, University of Illinois Press, Chicago, 1963. L. Boltzmann, Weitere Studien uber das Warmegleichgewicht unter Gasmoleculen. Sitzungsberichte Akad.Wiss., Vienna, Part II, 66¸ 275370, 1872. English translation in: G. S. Brush, Kinetic Theory, Vol.1-3, pp. 88-175, Pergamon Press, New York, 1965.
  • L. Boltzmann, Lectures on Gas Theory, Dover, New York, 1964.
  • O. Darrigol, Statistics and Combinatorics in Early Quantum Theory, Historical Studies in the Physical and Biological Sciences,19, 17-80, 1988; Statistics and Combinatorics in Early Quantum Theory, II: Early Symptoms of Indistinguishability and Holism, 21, 237298, 1991.
  • L. Brillouin, Maxwell Demon Cannot Operate: Information and Entropy I, J. Appl. Phys. 22, 334-337, 19 A. Ben-Naim, Entropy Demystified, World Scientific, New York, 2008.
  • M. Planck, Where Is Science Going, Ox Bow Press, Connecticut, 1981.
  • A. Ben-Naim, A Farewell to Entropy: Statistical Thermodynamics Based on Information, World Scientific, New York, 2008.
  • M. Planck, Zur Dynamik bewegter Systeme, Sitzungsber. Preuss. Akad. Wiss., 542; Ann. Physik 26, 1, 190 K. Mosengeil, Theorie der stationären Strahlung in einem gleichförmig bewegten Hohlraum, Ann. Physik 22, 876, 1907.
  • A. Einstein, Relativitätsprinzip und die aus demselben gezogenen Folgerungen, Jahrb. Radioaktivität und Elektron 5, 411, 1907. M. Laue, Das Relativitätsprinzip . Friedr. Vieweg & Sohn, Braunschweig , 19
  • F. Jüttner, Das Maxwellische Gesetz der Geschwindigkeitsverteilung in der Relativtheorie, Ann. Phys., Lyz. 34, 856, 1911.
  • W. Pauli, Theory of Relativity, p.135, Dover, 1958.
  • H. Poincaré, Sur la Dynamique de l’Electron, C. R. Acad. Sci. Paris 140, 1504-1508, 1905.
  • H. Poincaré, Sur la Dynamique de l’Electron, Rend. Circ. Mat. Palermo 21, 9-175, 1906.
  • A. Einstein, Zur Elecrodynamik bewegter Körper, Ann. der Phys. (Leipzig) 17, 891-921, 1905.
  • C. Liu, Einstein and Relativistic Thermodynamics in 1952: a Historical and Critical Study of a Strange Episode in the History of Modern Physics, BJHS 25, 185, 1992. H. Ott, Lorentz Transformation of Heat and Temperature , Zeitschrift fur Physik. 175, 70, 1963.
  • W. Schroeder, and H-J. Treder, The "Einstein-Laue" discussion. BJHS 27, 1113, 1992.
  • P. T. Landsberg, and G. E. A. Matsas, Laying the Ghost of the Relativistic Temperature Transformation, Phys. Lett. A. 23, 401, 1996.
  • M. Requardt, Thermodynamics Meets Special Relativity  or what is real in Physics? arXiv:0801.2639 v1[gr-qc], 17 Jan, 2008.
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There are 72 citations in total.

Details

Primary Language English
Journal Section Regular Original Research Article
Authors

Siavash Sohrab

Publication Date March 31, 2014
Published in Issue Year 2014

Cite

APA Sohrab, S. (2014). Some Implications of a Scale Invariant Model of Statistical Mechanics to Classical and Relativistic Thermodynamics. International Journal of Thermodynamics, 17(4), 233-248. https://doi.org/10.5541/ijot.585
AMA Sohrab S. Some Implications of a Scale Invariant Model of Statistical Mechanics to Classical and Relativistic Thermodynamics. International Journal of Thermodynamics. December 2014;17(4):233-248. doi:10.5541/ijot.585
Chicago Sohrab, Siavash. “Some Implications of a Scale Invariant Model of Statistical Mechanics to Classical and Relativistic Thermodynamics”. International Journal of Thermodynamics 17, no. 4 (December 2014): 233-48. https://doi.org/10.5541/ijot.585.
EndNote Sohrab S (December 1, 2014) Some Implications of a Scale Invariant Model of Statistical Mechanics to Classical and Relativistic Thermodynamics. International Journal of Thermodynamics 17 4 233–248.
IEEE S. Sohrab, “Some Implications of a Scale Invariant Model of Statistical Mechanics to Classical and Relativistic Thermodynamics”, International Journal of Thermodynamics, vol. 17, no. 4, pp. 233–248, 2014, doi: 10.5541/ijot.585.
ISNAD Sohrab, Siavash. “Some Implications of a Scale Invariant Model of Statistical Mechanics to Classical and Relativistic Thermodynamics”. International Journal of Thermodynamics 17/4 (December 2014), 233-248. https://doi.org/10.5541/ijot.585.
JAMA Sohrab S. Some Implications of a Scale Invariant Model of Statistical Mechanics to Classical and Relativistic Thermodynamics. International Journal of Thermodynamics. 2014;17:233–248.
MLA Sohrab, Siavash. “Some Implications of a Scale Invariant Model of Statistical Mechanics to Classical and Relativistic Thermodynamics”. International Journal of Thermodynamics, vol. 17, no. 4, 2014, pp. 233-48, doi:10.5541/ijot.585.
Vancouver Sohrab S. Some Implications of a Scale Invariant Model of Statistical Mechanics to Classical and Relativistic Thermodynamics. International Journal of Thermodynamics. 2014;17(4):233-48.