Relativistic Momentum and Manifestly Covariant Equipartition Theorem Revisited

2010 ◽  
Author(s):  
Guillermo Chacón-Acosta ◽  
Leonardo Dagdug ◽  
Hugo A. Morales-Técotl ◽  
H. A. Morales-Tecotl ◽  
L. A. Urena-Lopez ◽  
...  
Keyword(s):  
Equipartition Theorem ◽  
Relativistic Momentum

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.

Hamilton-Jacobi Theory

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Bbgky Hierarchy ◽  
Distribution Functions ◽  
Symplectic Integrators ◽  
Partition Functions ◽  
Von Neumann ◽  
Equipartition Theorem ◽  
Recurrence Theorem ◽  
Phase Amplitude ◽  
Canonical Ensembles

This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.

scholarly journals Shift a laser beam back and forth to exchange heat and work in thermodynamics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
John A. C. Albay ◽  
Zhi-Yi Zhou ◽  
Cheng-Hung Chang ◽  
Yonggun Jun
Keyword(s):  
Optical Feedback ◽  
Brownian Particle ◽  
Time Varying ◽  
Optical Technique ◽  
Work Related ◽  
Engine Efficiency ◽  
Confining Potential ◽  
Equipartition Theorem ◽  
Virtual Temperature ◽  
High Flexibility

AbstractAlthough the equivalence of heat and work has been unveiled since Joule’s ingenious experiment in 1845, they rarely originate from the same source in experiments. In this study, we theoretically and experimentally demonstrated how to use a high-precision optical feedback trap to combine the generation of virtual temperature and potential to simultaneously manipulate the heat and work of a small system. This idea was applied to a microscopic Stirling engine consisting of a Brownian particle under a time-varying confining potential and temperature. The experimental results justified the position and the velocity equipartition theorem, confirmed several theoretically predicted energetics, and revealed the engine efficiency as well as its trade-off relation with the output power. The small theory–experiment discrepancy and high flexibility of the swift change of the particle condition highlight the advantage of this optical technique and prove it to be an efficient way for exploring heat and work-related issues in the modern thermodynamics for small systems.

scholarly journals On the classical energy equipartition theorem

2000 ◽  
Vol 30 (1) ◽  
pp. 176-180 ◽  
Author(s):  
J. A. S. Lima ◽  
A. R. Plastino
Keyword(s):  
Classical Energy ◽  
Equipartition Theorem ◽  
Energy Equipartition

An alternate derivation of relativistic momentum

1986 ◽  
Vol 54 (9) ◽  
pp. 804-808 ◽  
Author(s):  
P. C. Peters
Keyword(s):  
Relativistic Momentum

Violation of Boltzmann Equipartition Theorem in Angular Phonon Phase Space Slows down Nanoscale Heat Transfer in Ultrathin Heterofilms

Nano Letters ◽  
2021 ◽  
Author(s):  
Anja Hanisch-Blicharski ◽  
Verena Tinnemann ◽  
Simone Wall ◽  
Fabian Thiemann ◽  
Thorben Groven ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Phase Space ◽  
Nanoscale Heat Transfer ◽  
Equipartition Theorem

scholarly journals On the equipartition theorem and black holes non-Gaussian entropies

2020 ◽  
Vol 35 (32) ◽  
pp. 2050266 ◽  
Author(s):  
Everton M. C. Abreu ◽  
Jorge Ananias Neto ◽  
Edésio M. Barboza ◽  
Albert C. R. Mendes ◽  
Bráulio B. Soares
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Heat Capacity ◽  
Algebraic Expression ◽  
Mathematical Form ◽  
Entropy Model ◽  
Standard Thermodynamic Functions ◽  
Mathematical Expressions ◽  
Equipartition Theorem ◽  
Non Gaussian

In this letter we have shown that, from the standard thermodynamic functions, the mathematical form of an equipartition theorem may be related to the algebraic expression of a particular entropy initially chosen to describe the black hole event horizon. Namely, we have different equipartition expressions for distinct statistics. To this end, four different mathematical expressions for the entropy have been selected to demonstrate our objective. Furthermore, a possible phase transition is observed in the heat capacity behavior of the Tsallis and Cirto entropy model.

scholarly journals Quantum analogue of energy equipartition theorem

2019 ◽  
Vol 52 (15) ◽  
pp. 15LT01 ◽  
Author(s):  
P Bialas ◽  
J Spiechowicz ◽  
J Łuczka
Keyword(s):  
Quantum Analogue ◽  
Equipartition Theorem ◽  
Energy Equipartition
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