Energy fluctuations of a Brownian particle freely moving in a liquid
arXiv:2403.01402 · doi:10.1016/j.physa.2024.129889
Abstract
We study the statistical properties of the variation of the kinetic energy of a spherical Brownian particle that freely moves in an incompressible fluid at constant temperature. Based on the underdamped version of the generalized Langevin equation that includes the inertia of both the particle and the displaced fluid, we derive an analytical expression for the probability density function of such a kinetic energy variation during an arbitrary time interval, which exactly amounts to the energy exchanged with the fluid in absence of external forces. We also determine all the moments of this probability distribution, which can be fully expressed in terms of a function that is proportional to the velocity autocorrelation function of the particle. The derived expressions are verified by means of numerical simulations of the stochastic motion of a particle in a viscous liquid with hydrodynamic backflow for representative values of the time-scales of the system. Furthermore, we also investigate the effect of viscoelasticity on the statistics of the kinetic energy variation of the particle, which reveals the existence of three distinct regimes of the energy exchange process depending on the values of the viscoelastic parameters of the fluid.
6 figures
References in corpus (20)
- Ensemble and Trajectory Thermodynamics: A Brief Introduction
- Integral fluctuation theorem for the housekeeping heat
- Work and heat probability distribution of an optically driven Brownian particle: Theory and experiments
- Large deviations of heat flow in harmonic chains
- Work and dissipation fluctuations near the stochastic resonance of a colloidal particle
- Markovian embedding of fractional superdiffusion
- Overdamped stochastic thermodynamics with multiple reservoirs
- Bound particle coupled to two thermostats
- The Fractional Langevin Equation: Brownian Motion Revisited
- On the stochastic thermodynamics of fractional Brownian motion
- Stochastic thermodynamics of Langevin systems under time-delayed feedback control: II. Nonequilibrium steady-state fluctuations
- Heat distribution function for motion in a general potential at low temperature
- Hydrodynamic memory can boost enormously driven nonlinear diffusion and transport
- The Heat Distribution in a Logarithm Potential
- A Rheological Analogue for Brownian Motion with Hydrodynamic Memory
- Heat fluctuations in equilibrium
- The Heat Distribution of the Underdamped Langevin Equation
- Stochastic energetics of a colloidal particle trapped in a viscoelastic bath
- Surmounting potential barriers: hydrodynamic memory hedges against thermal fluctuations in particle transport
- Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold