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Relativistic Brownian Motion
Jörn Dunkel, Peter Hänggi
Stimulated by experimental progress in high energy physics and astrophysics, the unification of relativistic and stochastic concepts has re-attracted considerable interest during t…
Time parameters and Lorentz transformations of relativistic stochastic processes
Jörn Dunkel, Peter Hänggi, Stefan Weber
Rules for the transformation of time parameters in relativistic Langevin equations are derived and discussed. In particular, it is shown that, if a coordinate-time parameterized pr…
Thermal equilibrium and statistical thermometers in special relativity
David Cubero, Jesús Casado-Pascual, Jörn Dunkel +2
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 candida…
Relative entropy, Haar measures and relativistic canonical velocity distributions
Jörn Dunkel, Peter Talkner, Peter Hänggi
The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting…
Relativistic diffusion processes and random walk models
Jörn Dunkel, Peter Talkner, Peter Hänggi
The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As well-known, the Gaussian transition probability den…
Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
Jörn Dunkel, Peter Hänggi
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy point-like Brownian pa…