Relativistic stochastic mechanics I: Langevin equation from observer's perspective

Abstract

Two different versions of relativistic Langevin equation in curved spacetime background are constructed, both are manifestly general covariant. It is argued that, from the observer's point of view, the version which takes the proper time of the Brownian particle as evolution parameter contains some conceptual issues, while the one which makes use of the proper time of the observer is more physically sound. The two versions of the relativistic Langevin equation are connected by a reparametrization scheme. In spite of the issues contained in the first version of the relativistic Langevin equation, it still permits to extract the physical probability distributions of the Brownian particles, as is shown by Monte Carlo simulation in the example case of Brownian motion in $(1+1)$-dimensional Minkowski spacetime.

23 pages. Title change and minor corrections

References in corpus (5)

• Relativistic Brownian Motion
• Time parameters and Lorentz transformations of relativistic stochastic processes
• Relativistic Fluctuation Theorems: Theory and explicit examples
• Stochastic Mechanics and the Unification of Quantum Mechanics with Brownian Motion
• Covariant Formulation of Non-linear Langevin Theory with Multiplicative Gaussian White Noises

Cited by in corpus (8)

• Relativistic stochastic mechanics II: Reduced Fokker-Planck equation in curved spacetime
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• General relativistic stochastic thermodynamics
• Stochastic dark matter: Covariant Brownian motion from Planckian discreteness
• The Kramers escape rate of phase transitions for the 6-dimensional Gauss-Bonnet AdS black hole with triple phases
• Fluctuation theorems in general relativistic stochastic thermodynamics
• Adiabatic Elimination in Relativistic Stochastic Mechanics