On transient relativistic thermodynamics and kinetic theory

1977 ◽  
Vol 357 (1688) ◽  
pp. 59-75 ◽  
Keyword(s):  
Heat Conduction ◽  
Kinetic Theory ◽  
Relativistic Theory ◽  
Speed Of Light ◽  
Equilibrium Thermodynamics ◽  
Dilute Gas ◽  
Fourier Heat Conduction ◽  
Relativistic Thermodynamics ◽  
Proper Account ◽  
Propagation Velocities

In the conventional Onsager formulation of non-equilibrium thermodynamics the Fourier heat conduction law is parabolic, and permits arbitrarily large propagation velocities for temperature discontinuities. While embarassing in a non-relativistic theory, this is unacceptable in a relativistic one. This paper presents a detailed discussion of the thermodynamics and (in the dilute gas limit) kinetic theory of such transients. When proper account of the two length scales involved is taken into account, the theory becomes hyperbolic; propagation velocities for a dilute gas never exceed √3/5 c = 0.775 c , where c is the speed of light.

scholarly journals Theories and heat pulse experiments of non-Fourier heat conduction

2016 ◽  
Vol 7 (2) ◽  
pp. 150-166 ◽  
Author(s):  
Péter Ván
Keyword(s):  
Heat Conduction ◽  
Heat Pulse ◽  
Theoretical Background ◽  
Point Of View ◽  
Experimental Basis ◽  
Equilibrium Thermodynamics ◽  
Fourier Heat Conduction ◽  
Non Equilibrium

Abstract The experimental basis and theoretical background of non-Fourier heat conduction is shortly reviewed from the point of view of non-equilibrium thermodynamics. The performance of different theories is compared in case of heat pulse experiments.

scholarly journals A case study of non-Fourier heat conduction using internal variables and GENERIC

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mátyás Szücs ◽  
Michal Pavelka ◽  
Róbert Kovács ◽  
Tamás Fülöp ◽  
Péter Ván ◽  
...  
Keyword(s):  
Heat Conduction ◽  
General Equation ◽  
Internal Variables ◽  
State Variables ◽  
Equilibrium Thermodynamics ◽  
Ginzburg Landau ◽  
Entropy Current ◽  
Fourier Heat Conduction ◽  
Non Equilibrium

Abstract Applying simultaneously the methodology of non-equilibrium thermodynamics with internal variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible–Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier’s law and its various extensions—the Maxwell–Cattaneo–Vernotte, Guyer–Krumhansl, Jeffreys type, Ginzburg–Landau (Allen–Cahn) type and ballistic–diffusive heat conduction equations—are derived in both formulations. Along these lines, a comparison of NET-IV and GENERIC is also performed. Our results may pave the way for microscopic/multiscale understanding of beyond-Fourier heat conduction and open new ways for numerical simulations of heat conduction problems.

The Boltzmann Equation and the H Theorem (1872–1875)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Heat Conduction ◽  
Boltzmann Equation ◽  
Transport Phenomena ◽  
Dilute Gas ◽  
The Boltzmann Equation ◽  
H Theorem ◽  
Irreversible Evolution

This chapter covers Boltzmann’s writings about the Boltzmann equation and the H theorem in the period 1872–1875, through which he succeeded in deriving the irreversible evolution of the distribution of molecular velocities in a dilute gas toward Maxwell’s distribution. Boltzmann also used his equation to improve on Maxwell’s theory of transport phenomena (viscosity, diffusion, and heat conduction). The bulky memoir of 1872 and the eponymous equation probably are Boltzmann’s most famous achievements. Despite the now often obsolete ways of demonstration, despite the lengthiness of the arguments, and despite hidden difficulties in the foundations, Boltzmann there displayed his constructive skills at their best.

Boltzmann’s Kinetic Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Statistical Physics ◽  
Neutron Transport ◽  
Condensed Matter ◽  
Relativistic Fluids ◽  
Classical Statistical Mechanics ◽  
Dilute Gas ◽  
Equilibrium Processes ◽  
The Boltzmann Equation

Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic introduction to the Boltzmann equation in the context of classical statistical mechanics shall be provided.

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