Communication: Beyond Boltzmann's H-theorem: Demonstration of the relaxation theorem for a non-monotonic approach to equilibrium

2012 ◽  
Vol 136 (2) ◽  
pp. 021101 ◽  
Author(s):  
James C. Reid ◽  
Denis J. Evans ◽  
Debra J. Searles
Keyword(s):  
Approach To Equilibrium ◽  
H Theorem ◽  
Relaxation Theorem

Approach to Equilibrium, the H-Theorem and Irreversibility

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Detailed Knowledge ◽  
Approach To Equilibrium ◽  
The Boltzmann Equation ◽  
H Theorem ◽  
Irreversible Evolution

Like most of the greatest equations in science, the Boltzmann equation is not only beautiful but also generous. Indeed, it delivers a great deal of information without imposing a detailed knowledge of its solutions. In fact, Boltzmann himself derived most if not all of his main results without ever showing that his equation did admit rigorous solutions. This Chapter illustrates one of the most profound contributions of Boltzmann, namely the famous H-theorem, providing the first quantitative bridge between the irreversible evolution of the macroscopic world and the reversible laws of the underlying microdynamics.

The Analogical Turn (1884–1887)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Boltzmann Equation ◽  
Statistical Mechanics ◽  
Mechanical System ◽  
Thermal Equilibrium ◽  
Special Kind ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Equipartition Theorem ◽  
Royal Road ◽  
H Theorem

This chapter recounts how Boltzmann reacted to Hermann Helmholtz’s analogy between thermodynamic systems and a special kind of mechanical system (the “monocyclic systems”) by grouping all attempts to relate thermodynamics to mechanics, including the kinetic-molecular analogy, into a family of partial analogies all derivable from what we would now call a microcanonical ensemble. At that time, Boltzmann regarded ensemble-based statistical mechanics as the royal road to the laws of thermal equilibrium (as we now do). In the same period, he returned to the Boltzmann equation and the H theorem in reply to Peter Guthrie Tait’s attack on the equipartition theorem. He also made a non-technical survey of the second law of thermodynamics seen as a law of probability increase.

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.

On Rates of Approach to Equilibrium

1953 ◽  
Vol 21 (10) ◽  
pp. 1888-1889 ◽  
Author(s):  
S. H. Bauer
Keyword(s):  
Approach To Equilibrium

The H-theorem for the entropy of waves

2021 ◽  
pp. 127315
Author(s):  
Eiichirou Kawamori
Keyword(s):  
H Theorem

Approach to Equilibrium of a Neutron Pulse in a Multiplying System

1965 ◽  
Vol 22 (2) ◽  
pp. 182-190 ◽  
Author(s):  
A. K. Ghatak ◽  
S. Pearlstein
Keyword(s):  
Neutron Pulse ◽  
Approach To Equilibrium

scholarly journals Nonlinear-cobweb dynamics in the approach to equilibrium

2004 ◽  
Vol 46 (1) ◽  
pp. 79-83 ◽  
Author(s):  
J. M. Gaffney ◽  
C. E. M. Pearce
Keyword(s):  
Linear Model ◽  
Approach To Equilibrium

AbstractWe discuss some propositions of Holmes and Manning relating to the evolution of price in a cobweb market approaching equilibrium. We find in particular that the detailed behaviour of the linear model is quite typical of nonlinear cobweb models.

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