Relativistic Langevin Equation derived from a particle-bath Lagrangian
arXiv:2107.07205 · doi:10.1088/1751-8121/ac3a33
Abstract
We show how a relativistic Langevin equation can be derived from a Lorentz-covariant version of the Caldeira-Leggett particle-bath Lagrangian. In one of its limits, we identify the obtained equation with the Langevin equation used in contemporary extensions of statistical mechanics to the near-light-speed motion of a Brownian particle in non-relativistic dissipative fluids. The proposed framework provides a more rigorous and first-principles form of the Langevin equation often quoted or postulated as ansatz in previous works. We then refine the aforementioned results by considering more terms in the particle-bath coupling, which improves the precision of the approximation for fully relativistic settings where not only the tagged particle but also the thermal bath motion is relativistic. We discuss the implications of the apparent breaking of space-time translation and parity invariance, showing that these effects are not necessarily in contradiction with the assumptions of statistical mechanics. The intrinsically non-Markovian character of the fully relativistic generalized Langevin equation derived here, and of the associated fluctuation-dissipation theorem, is also discussed.
References in corpus (30)
- Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies
- Bayes in the sky: Bayesian inference and model selection in cosmology
- Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene
- PolyChord: nested sampling for cosmology
- Lectures on hydrodynamic fluctuations in relativistic theories
- State-dependent diffusion: thermodynamic consistency and its path integral formulation
- New Extraction of the Cosmic Birefringence from the Planck 2018 Polarization Data
- Relativistic Brownian Motion
- Langevin equation with colored noise for constant-temperature molecular dynamics simulations
- Viscosity and dissipative hydrodynamics from effective field theory
- Heavy Quark Diffusion with Relativistic Langevin Dynamics in the Quark-Gluon Fluid
- Thermal equilibrium and statistical thermometers in special relativity
- Relativistic Dissipative Hydrodynamics: A Minimal Causal Theory
- Decoherence, discord and the quantum master equation for cosmological perturbations
- Dissipative quantum systems modeled by a two level reservoir coupling
- Generalized Langevin equation and fluctuation-dissipation theorem for particle-bath systems in external oscillating fields
- Stochastic trailing string and Langevin dynamics from AdS/CFT
- Time evolution of the fission-decay width under the influence of dissipation
- Universal linear and nonlinear electrodynamics of the Dirac fluid
- Mori-Zwanzig projection operator formalism for systems with time-dependent Hamiltonians
- Relativistic Harmonic Oscillator
- Relativistic Langevin Dynamics in Expanding Media
- Stochastic String Motion Above and Below the World Sheet Horizon
- Relativistic Brownian motion on a graphene chip
- Stochastic thermodynamics of relativistic Brownian motion
- Thermodynamic Laws and Equipartition Theorem in Relativistic Brownian Motion
- Non-Markovian large amplitude motion and nuclear fission
- Temperature dependence of nuclear fission time in heavy-ion fusion-fission reactions
- Probability density of fractional Brownian motion and the fractional Langevin equation with absorbing walls
- Quasirelativistic Langevin equation