Scale-Invariant Model of Boltzmann Statistical Mechanics and Generalized Thermodynamics

Some implications of a scale-invariant model of Boltzmann statistical mechanics to the laws of generalized thermodynamics are investigated. Through definition of stochastic Planck and Boltzmann universal constants, dimension of Kelvin absolute temperature T (degrees kelvin) is identified as a length (meters) associated with Wien wavelength T_β = λ_wβ of particle thermal oscillations. Hence, thermodynamic temperature and atomic mass of the field 𝔽_β at scale β provide internal measures of (extension, duration) of background space 𝕊_β+1 = 𝔽_β needed to define external space and time coordinates and atomic-mass-unit of 𝔽_β+1. Introduction of invariant internal thermodynamic spacetime and Boltzmann factor are in harmony with modern concepts of quantum gravity as deterministic dissipative dynamic system [73]. The connections between de Pretto number 8338 and Joule-Mayer mechanical equivalent of heat J_c = 4.169 kJ / kcal and universal gas constant R^o = 8338 J / kcal.m are identified leading to the modified mechanical equivalent of heat J = 2J_c = 8338 J / kcal . It is shown that with work defined as Helmholtz free energy W = F = U – TS, Helmholtz decomposition of total thermal energy into free heat U and latent heat pV results in modified form of the first law of thermodynamics Q = H = U- W = U + pV. Finally, by application of Boltzmann combinatorics method, entropy of ideal gas is expressed in terms of the number of Heisenberg-Kramers virtual oscillators as S = 4Nk in exact agreement with predicted entropy of black hole by Major and Setter [159].

Some implications of a scale-invariant model of Boltzmann statistical mechanics to the laws of generalized thermodynamics are investigated. Through definition of stochastic Planck and Boltzmann universal constants, dimension of Kelvin absolute temperature T (degrees kelvin) is identified as a length (meters) associated with Wien wavelength T_β = λ_wβ of particle thermal oscillations. Hence, thermodynamic temperature and atomic mass of the field 𝔽_β at scale β provide internal measures of (extension, duration) of background space 𝕊_β+1 = 𝔽_β needed to define external space and time coordinates and atomic-mass-unit of 𝔽_β+1. Introduction of invariant internal thermodynamic spacetime and Boltzmann factor are in harmony with modern concepts of quantum gravity as deterministic dissipative dynamic system [73]. The connections between de Pretto number 8338 and Joule-Mayer mechanical equivalent of heat J_c = 4.169 kJ / kcal and universal gas constant R^o = 8338 J / kcal.m are identified leading to the modified mechanical equivalent of heat J = 2J_c = 8338 J / kcal . It is shown that with work defined as Helmholtz free energy W = F = U – TS, Helmholtz decomposition of total thermal energy into free heat U and latent heat pV results in modified form of the first law of thermodynamics Q = H = U- W = U + pV. Finally, by application of Boltzmann combinatorics method, entropy of ideal gas is expressed in terms of the number of Heisenberg-Kramers virtual oscillators as S = 4Nk in exact agreement with predicted entropy of black hole by Major and Setter [159].

Generalized thermodynamics entropy Absolute temperature scale Spacetime Quantum nature of space and time Quantum gravity T.O.E

Generalized thermodynamics entropy Absolute temperature scale Spacetime Quantum nature of space and time Quantum gravity T.O.E