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

2014 ◽  
Vol 17 (4) ◽  
pp. 233 ◽  
Author(s):  
Siavash H. Sohrab
Keyword(s):  
Statistical Mechanics ◽  
Scale Invariant ◽  
Invariant Model ◽  
Relativistic Thermodynamics

scholarly journals Some Implications of a Scale Invariant Model of Statistical Mechanics to Boltzmann versus Shannon Entropy in Thermodynamics and Information Theory

2021 ◽  
Vol 20 ◽  
pp. 56-65
Author(s):  
Siavash H. Sohrab
Keyword(s):  
Information Theory ◽  
Statistical Mechanics ◽  
Comparative Study ◽  
Shannon Entropy ◽  
Scale Invariant ◽  
Invariant Model ◽  
Shannon's Entropy ◽  
The Third ◽  
Third Law Of Thermodynamics ◽  
Third Law

A scale invariant model of statistical mechanics is applied for a comparative study of Boltzmann’s entropy in thermodynamics versus Shannon’s entropy in information theory. The implications of the model to the objective versus subjective aspects of entropy as well as Nernst-Planck statement of the third law of thermodynamics are also discussed

On a Scale-Invariant Model of Statistical Mechanics and the Laws of Thermodynamics

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Siavash H. Sohrab
Keyword(s):  
Statistical Mechanics ◽  
Thermal Energy ◽  
Thermodynamic System ◽  
Ideal Gas ◽  
Absolute Temperature ◽  
Scale Invariant ◽  
Invariant Model ◽  
Definition Of ◽  
Classical Thermodynamics ◽  
Total Thermal Energy

A scale-invariant model of statistical mechanics is applied to describe modified forms of zeroth, first, second, and third laws of classical thermodynamics. Following Helmholtz, the total thermal energy of the thermodynamic system is decomposed into free heat U and latent heat pV suggesting the modified form of the first law of thermodynamics Q = H = U + pV. Following Boltzmann, entropy of ideal gas is expressed in terms of the number of Heisenberg–Kramers virtual oscillators as S = 4 Nk. Through introduction of stochastic definition of Planck and Boltzmann constants, Kelvin absolute temperature scale T (degree K) is identified as a length scale T (m) that is related to de Broglie wavelength of particle thermal oscillations. It is argued that rather than relating to the surface area of its horizon suggested by Bekenstein (1973, “Black Holes and Entropy,” Phys. Rev. D, 7(8), pp. 2333–2346), entropy of black hole should be related to its total thermal energy, namely, its enthalpy leading to S = 4Nk in exact agreement with the prediction of Major and Setter (2001, “Gravitational Statistical Mechanics: A Model,” Classical Quantum Gravity, 18, pp. 5125–5142).

scholarly journals Connecting complex networks to nonadditive entropies

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. M. de Oliveira ◽  
Samuraí Brito ◽  
L. R. da Silva ◽  
Constantino Tsallis
Keyword(s):  
Statistical Mechanics ◽  
Energy Distribution ◽  
Complex Networks ◽  
Wide Class ◽  
Scale Invariant ◽  
Nonlocal Effects ◽  
Geometric Problem ◽  
Exponential Factor ◽  
Research Areas ◽  
Quasi Stationary State

AbstractBoltzmann–Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving nonlocal space–time entanglement. Its generalization based on nonadditive q-entropies adequately handles a wide class of such systems. We show here that scale-invariant networks belong to this class. We numerically study a d-dimensional geographically located network with weighted links and exhibit its ‘energy’ distribution per site at its quasi-stationary state. Our results strongly suggest a correspondence between the random geometric problem and a class of thermal problems within the generalised thermostatistics. The Boltzmann–Gibbs exponential factor is generically substituted by its q-generalisation, and is recovered in the $$q=1$$ q = 1 limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas.

Invariant Forms of Conservation Equations and Some Examples of Their Exact Solutions

2014 ◽  
Author(s):  
Siavash H. Sohrab
Keyword(s):  
Momentum Conservation ◽  
Enskog Equation ◽  
Cauchy Stress ◽  
Cauchy Stress Tensor ◽  
Scale Invariant ◽  
Spherical Droplet ◽  
Conservation Equations ◽  
Invariant Model ◽  
Cylindrically Symmetric ◽  
Tangential Forces

A scale-invariant model of statistical mechanics is described leading to invariant Boltzmann equation and the corresponding invariant Enskog equation of change. A modified form of Cauchy stress tensor for fluid is presented such that in the limit of vanishing intermolecular spacing all tangential forces vanish in accordance with perceptions of Cauchy and Poisson. The invariant forms of mass, thermal energy, linear momentum, and angular momentum conservation equations derived from invariant Enskog equation of change are described. Also, some exact solution of the conservation equations for the problems of normal shock, flow over a flat plate, and flow within a spherical droplet located at the stagnation point of opposed cylindrically-symmetric gaseous jets are presented.

Invariant Forms of Conservation Equations for Reactive Fields and Hydro-Thermo-Diffusive Theory of Laminar Flames

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Siavash H. Sohrab
Keyword(s):  
Angular Momentum ◽  
Propagation Speed ◽  
Premixed Flame ◽  
Laminar Flames ◽  
Enskog Equation ◽  
Scale Invariant ◽  
Propagation Models ◽  
Conservation Equations ◽  
Invariant Model ◽  
Good Agreement

A scale-invariant model of statistical mechanics is described leading to invariant Enskog equation of change that is applied to derive invariant forms of conservation equations for mass, thermal energy, linear momentum, and angular momentum in chemically reactive fields. Modified hydro-thermo-diffusive theories of laminar premixed flames for (1) rigid-body and (2) Brownian-motion flame propagation models are presented and are shown to be mathematically equivalent. The predicted temperature profile, thermal thickness, and propagation speed of laminar methane–air premixed flame are found to be in good agreement with existing experimental observations.

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