Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle

Abstract

In this work, we study the nonequilibrium statistical properties of the relaxation dynamics of a nanoparticle trapped in a harmonic potential. We report an exact time-dependent analytical solution to the Langevin dynamics that arises from the stochastic differential equation of our system's energy in the underdamped regime. By utilizing this stochastic thermodynamics approach, we are able to completely describe the heat exchange process between the nanoparticle and the surrounding environment. As an important consequence of our results, we observe the validity of the heat exchange fluctuation theorem (XFT) in our setup, which holds for systems arbitrarily far from equilibrium conditions. By extending our results for the case of $N$ noninterating nanoparticles, we perform analytical asymptotic limits and direct numerical simulations that corroborate our analytical predictions.

arXiv comment11 pages, 6 figures

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• A microscopic theory of Curzon-Ahlborn heat engine
• Quantum-classical correspondence principle for heat distribution in quantum Brownian motion
• Stochastic energetics of a colloidal particle trapped in a viscoelastic bath
• Heat distribution in open quantum systems with maximum entropy production
• Detailed fluctuation theorem bounds apparent violations of the second law
• Information bound for entropy production from the detailed fluctuation theorem
• Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs
• Stochastic thermodynamics of nonharmonic oscillators in high vacuum
• Relation between fluctuations and efficiency at maximum power for small heat engines
• Temperature fluctuations in mesoscopic systems
• Single Particle Thermodynamics with Levitated Nanoparticles
• Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold