The spatially one-dimensional relativistic Ornstein-Uhlenbeck process in an arbitrary inertial frame

Barbachoux, Cécile; Debbasch, Fabrice; Rivet, J. P.

doi:10.1007/s100510170348

Cited by 32 publications

(34 citation statements)

References 6 publications

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“…• One constructs relativistically acceptable Markov processes in phase space by considering not only the position coordinate X (t) of the diffusing particle, but also its momentum coordinate P(t) [11][12][13][14][15][16][17][18][19][20][21][22]24,26,31,32,[220][221][222][332][333][334][335][336][337][338].…”

Section: Relativistic Diffusion Processes: Problems and General Stratmentioning

confidence: 99%

“…As an alternative to non-Markovian diffusion models in spacetime, one can consider relativistic Markov processes in phase space [11][12][13][14][15][16][17][18][19][20][21][22]24,26,[31][32][33][34][220][221][222][332][333][334][335][336][337][338]. Typical examples are processes described by Fokker-Planck equations (FPEs) or Langevin equations [11][12][13][14][15]17,18,20,21,[24][25][26][31][32][33][34][391][392][393][394][395].…”

Section: Relativistic Markov Processes In Phase Spacementioning

confidence: 99%

“…A complementary approach towards relativistic stochastic processes in phase space starts from Langevin equations [11][12][13][14][15]17,18,20,21,[24][25][26]31,32,[391][392][393][394][395]. Stochastic differential equations of the Langevin type yield explicit sample trajectories for the stochastic motion of a relativistic Brownian particle.…”

Section: Relativistic Markov Processes In Phase Spacementioning

confidence: 99%

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Relativistic Brownian motion

2009

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a b s t r a c tOver the past one hundred years, Brownian motion theory has contributed substantially to our understanding of various microscopic phenomena. Originally proposed as a phenomenological paradigm for atomistic matter interactions, the theory has since evolved into a broad and vivid research area, with an ever increasing number of applications in biology, chemistry, finance, and physics. The mathematical description of stochastic processes has led to new approaches in other fields, culminating in the path integral formulation of modern quantum theory. Stimulated by experimental progress in high energy physics and astrophysics, the unification of relativistic and stochastic concepts has re-attracted considerable interest during the past decade. Focusing on the framework of special relativity, we review, here, recent progress in the phenomenological description of relativistic diffusion processes. After a brief historical overview, we will summarize basic concepts from the Langevin theory of nonrelativistic Brownian motions and discuss relevant aspects of relativistic equilibrium thermostatistics. The introductory parts are followed by a detailed discussion of relativistic Langevin equations in phase space. We address the choice of time parameters, discretization rules, relativistic fluctuationdissipation theorems, and Lorentz transformations of stochastic differential equations. The general theory is illustrated through analytical and numerical results for the diffusion of free relativistic Brownian particles. Subsequently, we discuss how Langevin-type equations can be obtained as approximations to microscopic models. The final part of the article is dedicated to relativistic diffusion processes in Minkowski spacetime. Since the velocities of relativistic particles are bounded by the speed of light, nontrivial relativistic Markov processes in spacetime do not exist; i.e., relativistic generalizations of the nonrelativistic diffusion equation and its Gaussian solutions must necessarily be non-Markovian. We compare different proposals that were made in the literature and discuss their respective benefits and drawbacks. The review concludes with a summary of open questions, which may serve as a starting point for future investigations and extensions of the theory.

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Section: Relativistic Diffusion Processes: Problems and General Stratmentioning

confidence: 99%

Section: Relativistic Markov Processes In Phase Spacementioning

confidence: 99%

Section: Relativistic Markov Processes In Phase Spacementioning

confidence: 99%

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Relativistic Brownian motion

2009

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“…This proof [10] is actually rather particular because it has been given in the context of relativistic stochastic processes only, and more precisely for the distribution function associated to the so-called relativistic OrnsteinUhlenbeck process, which is a toy-model of relativistic diffusion. As such, this proof makes extensive use of stochastic calculus.…”

Section: Discussionmentioning

confidence: 99%

“…In other words, deterministic evolution equations establish a one-to-one correspondence between the histories and the states of the system at a given time in R. Thus averaging over histories comes down in such cases to averaging over states. The matter is more complicated if the microscopic evolution equations are stochastic, typically involving some random 'noise' (for an example of stochastic process in the relativistic framework, we refer the reader to [9] and [10]). For a given realization of the noise i.e.…”

Section: Relativistic Covariant Ensemblesmentioning

confidence: 99%

Invariance of the relativistic one-particle distribution function

Debbasch¹,

Rivet

Leeuwen³

2001

Physica A: Statistical Mechanics and its Applications

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Behçet’s disease: immunological relevance with arthritis of ankylosing spondylitis

et al. 2012

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Behçet's disease (BD) is a multi-system inflammatory disorder, in which cytokine balance is polarized to Th1. In this study, the cell surface molecule expression, Th1/Th2, inflammatory cytokine levels in blood, and synovial fluid of CD3(+) T lymphocytes in BD were investigated. The study group consisted of 10 BD, 10 ankylosing spondylitis (AS) patients with peripheral arthritis, and 10 healthy subjects. Expression of cell surface molecules, intracellular IL-2, IL-5, IL-8, IL-10, IL-12, IFN-γ, and TNF-α levels in CD3(+) T lymphocytes were determined by flow cytometry in synovial and peripheral blood mononuclear cells (PBMCs). Synovial and plasma cytokine levels were measured by ELISA and CBA. In PBMCs, CD4, CD25, HLA-DR expression and intracellular IL-12, and TNF-α levels of CD3(+) T lymphocytes were statistically increased in BD patients compared to healthy subjects. Compare to AS patients, CD25 and HLA-DR surface expression and intracellular IFN-γ and TNF-α levels in T cells were significantly elevated in BD patients. In BD patients, there was an increase in IL-8 secretion; however, in AS patients, both Th1- and Th2-type cytokines were increased compare to healthy subjects. Intracellular cytokine expression did not show any difference in BD patients; however, IL-12 content of synovial fluid was significantly increased compared to AS patients. Our findings revealed that Th1 polarization occurred in both peripheral blood and synovial fluid of BD patients with arthritis. It is found no difference between synovial fluid analysis of BD and AS patients, showing the similarities in the pathogenesis of both diseases.

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The spatially one-dimensional relativistic Ornstein-Uhlenbeck process in an arbitrary inertial frame

Cited by 32 publications

References 6 publications

Relativistic Brownian motion

Relativistic Brownian motion

Invariance of the relativistic one-particle distribution function

Behçet’s disease: immunological relevance with arthritis of ankylosing spondylitis

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