Heat distribution of relativistic Brownian motion

Paraguassú, Pedro V.; Morgado, Welles A. M.

doi:10.1140/epjb/s10051-021-00214-8

Cited by 8 publications

(18 citation statements)

References 49 publications

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“…For equation (30), much like in the previous case, let us proceed in a term-by-term fashion. Firstly, the term…”

Section: Lorentz Covariancementioning

confidence: 99%

“…Thus, we showed that all terms appearing in equation ( 30) are Lorentz-covariant fourvectors. This allows us to rewrite our relativistic Langevin equation (30) in explicitly Lorentzcovariant form:…”

Section: Lorentz Covariancementioning

confidence: 99%

“…Time and space inversion symmetry are violated individually. However, since equation (15b) is invariant with respect to a simultaneous inversion of both, and the function which approximates the general solution (equation ( 19)), is too, we can expect equation (30) to be invariant with respect to inversion of both time and space, combined together. This is not uncommon: CPT [61,62] is widely considered to be a fundamental symmetry of the relativistic theories while symmetries with respect to time and space inversion are individually violated even in simple Newtonian cases: a disk spinning clockwise is spinning counter-clockwise in the mirror Universe, and a counter-clockwise spinning disk is spinning clockwise if we reverse the arrow of time.…”

Section: Time Inversion and Paritymentioning

confidence: 99%

“…In this section we shall briefly address the apparent breaking of translational invariance in equation (30). Let us first recall what kind of translational invariance is relevant here.…”

Section: Space-time Translation Invariancementioning

confidence: 99%

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Relativistic Langevin equation derived from a particle-bath Lagrangian

Petrosyan¹,

Zaccone²

2022

J. Phys. A: Math. Theor.

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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 tagged particle in non-relativistic dissipative fluids. The proposed framework provides a more rigorous and first-principles form of the weakly-relativistic and partially-relativistic Langevin equations often quoted or postulated as ansatz in previous works. We then refine the aforementioned results to obtain a generalized Langevin equation valid for the case of both fully-relativistic particle and bath, using an analytical approximation obtained from numerics where the Fourier modes of the bath are systematically replaced with covariant plane-wave forms with a length-scale relativistic correction that depends on the space-time trajectory in a parabolic way. 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 generalised Langevin equation derived here, and of the associated fluctuation-dissipation theorem, is also discussed.

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“…For equation (30), much like in the previous case, let us proceed in a term-by-term fashion. Firstly, the term…”

Section: Lorentz Covariancementioning

confidence: 99%

Section: Lorentz Covariancementioning

confidence: 99%

Section: Time Inversion and Paritymentioning

confidence: 99%

“…In this section we shall briefly address the apparent breaking of translational invariance in equation (30). Let us first recall what kind of translational invariance is relevant here.…”

Section: Space-time Translation Invariancementioning

confidence: 99%

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Relativistic Langevin equation derived from a particle-bath Lagrangian

Petrosyan¹,

Zaccone²

2022

J. Phys. A: Math. Theor.

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“…Other effects on the heat distribution for Brownian particles, e.g. nonlinear potentials [44][45][46], inertia [47][48][49][50][51], relativistic motion [52], and non-isothermal transformations [53], have also been addressed theoretically. Furthermore, heat fluctuations have been studied for active matter systems, such as active chains in viscous heat baths [54], Brownian particles embedded in active media [55,56], and activity-driven harmonic chains [57].…”

Section: Introductionmentioning

confidence: 99%

Stochastic energetics of a colloidal particle trapped in a viscoelastic bath

Darabi,

Ferrer,

Gomez-Solano

2023

New J. Phys.

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We investigate the statistics of the fluctuations of the energy transfer between an overdamped Brownian particle, whose motion is confined by a stationary harmonic potential, and a surrounding viscoelastic fluid at constant temperature. We derive an analytical expression for the probability density function of the energy exchanged with the fluid over a finite time interval, which implicitly involves the friction memory kernel that encodes the coupling with such a non-Markovian environment, and reduces to the well known expression for the heat distribution in a viscous fluid. We show that, while the odd moments of this distribution are zero, the even moments can be explicitly expressed in terms of the autocorrelation function of the particle position, which generally exhibits a non-mono-exponential decay when the fluid bath is viscoelastic. Our results are verified by experimental measurements for an optically-trapped colloidal bead in semidilute micellar and polymer solutions, finding and excellent agreement for all time intervals over which the energy exchange takes place.

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