One-dimensional non-relativistic and relativistic Brownian motions: a microscopic collision model

Dunkel, Jörn; Hänggi, Peter

doi:10.1016/j.physa.2006.07.013

Cited by 33 publications

(80 citation statements)

References 51 publications

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“…The Jüttner distribution had been accepted for many years [5], [26]- [30], but from the 80's some authors have raised their objections to this distribution [31]- [35].…”

Section: From Jüttner Distribution To Phenomenological Relativistic Tmentioning

confidence: 99%

Notes on thermodynamics in special relativity

Przanowski¹,

Tosiek²

2011

Phys. Scr.

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Foundations of thermodynamics in special theory of relativity are considered. We argue that from the phenomenological point of view the correct relativistic transformations of heat and absolute temperature are given by the formulas proposed by H. Ott, H. Arzeliès and C. Møller. It is shown that the same transformation rules can be also found from the relativistic Gibbs distribution for ideal gas. This distribution has been recently verified by the computer simulations. Phenomenological and statistical thermometers in relativistic thermodynamics are analyzed.

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“…The Jüttner distribution had been accepted for many years [5], [26]- [30], but from the 80's some authors have raised their objections to this distribution [31]- [35].…”

Section: From Jüttner Distribution To Phenomenological Relativistic Tmentioning

confidence: 99%

Notes on thermodynamics in special relativity

Przanowski¹,

Tosiek²

2011

Phys. Scr.

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“…For example, a recently discussed alternative to Eq. (2) is the ''modified'' Jüttner function [18,19] The distribution (3) can be obtained, e.g., by combining a maximum relative entropy principle and Lorentz symmetry [20]. Compared with f J at the same parameter values J MJ & 1=m, the modified PDF f MJ exhibits a significantly lower particle population in the high energy tail because of the additional 1=E prefactor.…”

mentioning

confidence: 99%

“…For example, a recently discussed alternative to Eq. (2) is the ''modified'' Jüttner function [18,19] …”

mentioning

confidence: 99%

Thermal Equilibrium and Statistical Thermometers in Special Relativity

et al. 2007

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There is an intense debate in the recent literature about the correct generalization of Maxwell's velocity distribution in special relativity. The most frequently discussed candidate distributions include the Jüttner function as well as modifications thereof. Here we report results from fully relativistic one-dimensional molecular dynamics simulations that resolve the ambiguity. The numerical evidence unequivocally favors the Jüttner distribution. Moreover, our simulations illustrate that the concept of ''thermal equilibrium'' extends naturally to special relativity only if a many-particle system is spatially confined. They make evident that ''temperature'' can be statistically defined and measured in an observer frame independent way. DOI: 10.1103/PhysRevLett.99.170601 PACS numbers: 05.70.ÿa, 02.70.Ns, 03.30.+p At the beginning of the last century, it was commonly accepted that the one-particle velocity distribution of a dilute gas in equilibrium is described by the Maxwellian probability density function (PDF)[m: rest mass of a gas particle; v: velocity; T k B ÿ1 : temperature; k B : Boltzmann constant; d: space dimension; throughout, we adopt natural units such that the speed of light c 1]. When Einstein [1,2] had formulated the theory of special relativity (SR) in 1905, Planck and others noted immediately that f M is in conflict with the fundamental relativistic postulate that velocities cannot exceed the light speed c. A first solution to this problem was put forward by Jüttner [3]. Starting from a maximum entropy principle, he proposed the following relativistic generalization of Maxwell's PDF:[Z J Z J m; J ; d : normalization constant; E m v m 2 p 2 1=2 : relativistic particle energy; p mv v : momentum with Lorentz factor v 1 ÿ v 2 ÿ1=2 , jvj < 1]. Jüttner's distribution (2) became widely accepted among theorists during the first threequarters of the 20th century [4 -8]-although a rigorous microscopic derivation is lacking due to the difficulty of formulating a relativistically consistent Hamilton mechanics of interacting particles [9][10][11][12][13]. Doubts about the Jüttner function f J began to arise in the 1980s, when Horwitz et al. [14,15] proposed a ''manifestly covariant'' relativistic Boltzmann equation, whose stationary solution differs from Eq. (2) and, in particular, predicts a different mean energy-temperature relation in the ultrarelativistic limit T ! 1 [16]. Since then, partially conflicting results and proposals from other authors [17][18][19][20][21] have led to an increasing confusion as to which distribution actually represents the correct generalization of the Maxwellian (1). For example, a recently discussed alternative to Eq. (2) is the ''modified'' Jüttner function [18,19] The distribution (3) can be obtained, e.g., by combining a maximum relative entropy principle and Lorentz symmetry [20]. Compared with f J at the same parameter values J MJ & 1=m, the modified PDF f MJ exhibits a significantly lower particle population in the high energy tail because of the additional 1=E pre...

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“…Numerical studies are also not decisive due to the arbitrariness in the choice of time parameters [17,23] or discretization rules [24,25,26]. Therefore, at this stage we are obliged to accept the arbitrariness in the choice of reference density.…”

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confidence: 99%

Time parametrization and stationary distributions in a relativistic gas

Ghodrat

Montakhab

2010

Phys. Rev. E

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In this paper we consider the effect of different time parameterizations on the stationary velocity distribution function for a relativistic gas. We clarify the distinction between two such distributions, namely the Jüttner and the modified Jüttner distributions. Using a recently proposed model of a relativistic gas, we show that the obtained results for the proper-time averaging does not lead to modified Jüttner distribution (as recently conjectured), but introduces only a Lorentz factor γ to the well-known Jüttner function which results from observer-time averaging. We obtain results for rest frame as well as moving frame in order to support our claim.

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One-dimensional non-relativistic and relativistic Brownian motions: a microscopic collision model

Cited by 33 publications

References 51 publications

Notes on thermodynamics in special relativity

Notes on thermodynamics in special relativity

Thermal Equilibrium and Statistical Thermometers in Special Relativity

Time parametrization and stationary distributions in a relativistic gas

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