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Siavash H. Sohrab

Northwestern University

USA

Published on 11 October 2021 DOI : 10.21494/ISTE.OP.2021.0743

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* = 2*J*_{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* = 4*N*k 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* = 2*J*_{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* = 4*N*k 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