Non-linear relativistic diffusions

Abstract

We obtain a non-linear generalization of the relativistic diffusion of particles with spin. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic invariance and an interpretation of the solution as a probability distribution substantially restrict the class of admissible non-linear diffusion equations. We consider relativistic invariant as well as covariant frame dependent diffusion equations with a drift. In the latter case we show that there can exist stationary solutions of the diffusion equation besides the equilibrium solution corresponding to the quantum or Tsallis distributions. We define the relative entropy as a function of the diffusion probability and prove that it is monotonically decreasing in time when the diffusion tends to the equilibrium. We discuss its relation to the thermodynamic behavior of diffusing particles.

20 pages, the version to appear in Physica A

References in corpus (16)

• Non Linear Kinetics underlying Generalized Statistics
• Anomalous diffusion in the presence of external forces: exact time-dependent solutions and entropy
• Relativistic Brownian Motion
• Generalized thermodynamics and Fokker-Planck equations. Applications to stellar dynamics, two-dimensional turbulence and Jupiter's great red spot
• Kinetics of Bose-Condensation
• Equilibrium Distribution of Heavy Quarks in Fokker-Planck Dynamics
• Reionization and cosmic microwave background distortions: a complete treatment of second order Compton scattering
• Anomalous Transport Processes in Anisotropically Expanding Quark-Gluon Plasmas
• Some Bounds upon Nonextensivity Parameter Using the Appropriate Generalized Distribution Functions
• Diffusion and local deconfinement in relativistic systems
• Relativistic diffusion
• Relativistic diffusion with friction on a pseudoriemannian manifold
• Generalized Thermostatistics and Bose-Einstein Condensation
• Energy and entropy of relativistic diffusing particles
• Master Equation for Electromagnetic Dissipation and Decoherence of Density Matrix
• Relativistic diffusion of elementary particles with spin

Cited by in corpus (6)

• Relative Fisher information in some central potentials
• Einstein gravity of a diffusing fluid
• Brownian motion at the speed of light: a Lorentz invariant family of processes
• Inhomogeneous Boltzmann equations: distance, asymptotics and comparison of the classical and quantum cases
• Temperature fluctuations in an inhomogeneous diffusive fluid
• Information analysis in free and confined harmonic oscillator