Scale-Invariant Model of Boltzmann Statistical Mechanics and Generalized Thermodynamics (original) (raw)
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International Journal of Thermodynamics, 2014
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.
Universal nature of Boltzmann statistical mechanics, generalized thermodynamics, quantum mechanics, spacetime, black hole mechanics, Shannon information theory, Faraday lines of force, and Banach-Tarski paradox (BTP) are studied. The nature of matter and Dirac anti-matter are described in terms of states of compression and rarefaction of physical space, Aristotle fifth element, or Casimir vacuum identified as a compressible tachyonic fluid. The model is in harmony with perceptions of Plato who believed that the world was formed from a formless primordial medium that was initially in a state of total chaos or "Tohu Vavohu" (Sohrab, in Int J Mech 8:873-84, [1]. Hierarchies of statistical fields from photonic to cosmic scales lead to universal scale-invariant Schrödinger equation thus allowing for new perspectives regarding connections between classical mechanics, quantum mechanics, and chaos theory. The nature of external physical time and its connections to internal thermodynamics time and Rovelli thermal time are described. Finally, some implications of renormalized Planck distribution function to economic systems are examined. Keywords Thermodynamics. Quantum mechanics. Anti-matter. Spacetime. Thermal time. Information theory. Faraday lines of force. Banach-Tarski paradox. T.O.E.
International Journal of Thermal Sciences, 1999
A scale-invariant statistical theory of fields is presented that leads to invariant definition of density, velocity, temperature, and pressure. The definition of Boltzmann constant is introduced as kk-k = rakV'k C = 1.381"10-23 J-K-1, suggesting that the Kelvin absolute temperature scale is equivalent to a length scale. Two new state variables called the reversible heat Qrev = TS and the reversible work Wrev-PV are introduced. The modified forms of the first and second law of thermodynamics are presented. The microscopic definition of heat (work) is presented as the kinetic energy due to the random (peculiar) translational, rotational, and pulsational motions. The Gibbs free energy of an element at scale/3 is identified as the total system energy at scale (/3-1), thus leading to an invariant form of the first law of thermodynamics Uf~ = Q~-W~-I-Ne~ U~-I. ~)1999 [~ditions scientifiques et mfidicales Elsevier SAS. fundamental thermodynamics / first and second laws / invariant form / statistical thermodynamics / thermophysical characteristics
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