Relativistic Fluctuation Theorems: Theory and explicit examples

Abstract

To reveal how nonequilibrium physics and relativity theory intertwine, this articles studies relativistic Brownian motion under cosmic expansion. Two fluctuation theorems for the entropy ds, which is locally produced in this extreme nonequilibrium situation, are presented and proven. The first, <exp(-ds)>=1, is a generalization of the second law of thermodynamics, that remains valid at relativistic particle energies and under high cosmic expansion rates. From this relation follows, that the probability to observe a local reduction of entropy is exponentially small even if the universe was to recollapse. For the special case of the Einstein-de Sitter universe an additional relation, <exp(-ds-dh)>=1, is derived which holds simultaneously with the first relation and where dh is proportional to the Hubble constant. Furthermore, the fluctuation theorems are shown to provide a physical criterion to resolve the known discretization dilemma arising in special-relativistic Brownian motion. Explicit examples and a general method for the computation of non-Gaussian entropy fluctuations are provided.

27 pages, 6 figures, Comptes rendus - Physique

References in corpus (16)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• A nonequilibrium equality for free energy differences
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Fluctuation theorem for stochastic dynamics
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Path ensembles averages in systems driven far-from-equilibrium
• Heavy-Quark Probes of the Quark-Gluon Plasma at RHIC
• An Extension of the Fluctuation Theorem
• Theory of the Relativistic Brownian Motion. The (1+1)-Dimensional Case
• Theory of Relativistic Brownian Motion: The (1+3)-Dimensional Case
• The Origin of Time Asymmetry
• Time-symmetric fluctuations in nonequilibrium systems
• Arrows of Time and Chaotic Properties of the Cosmic Background Radiation

Cited by in corpus (12)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Relativistic Brownian Motion
• Fluctuation and dissipation in de Sitter space
• One-dimensional nonrelativistic and relativistic Brownian motions: A microscopic collision model
• Stochastic thermodynamics of relativistic Brownian motion
• Quantum work statistics of charged Dirac particles in time-dependent fields
• Stationarity, soft ergodicity, and entropy in relativistic systems
• Relativistic stochastic mechanics I: Langevin equation from observer's perspective
• Fluctuation theorem for entropy production during effusion of a relativistic ideal gas
• Promoting Fluctuation Theorems into Covariant Forms
• Fluctuation theorems in general relativistic stochastic thermodynamics
• Work and work-energy theorem in curved spacetime