Stochastic thermodynamics of nonharmonic oscillators in high vacuum

Domingos S. P. Salazar and Sérgio A. Lira
Phys. Rev. E 99, 062119 – Published 20 June 2019

Abstract

We perform an analytic study on the stochastic thermodynamics of a small classical particle trapped in a time-dependent single-well potential in the highly underdamped limit. It is shown that the nonequilibrium probability density function for the system's energy is a Maxwell-Boltzmann distribution (as in equilibrium) with a closed form time-dependent effective temperature and fractional degrees of freedom. We also find that the solvable model satisfies the Crooks fluctuation theorem, as expected. Moreover, we compute the average work in this isothermal process and characterize analytically the optimal protocol for minimum work. The optimal protocol presents an initial and a final jump which correspond to adiabatic processes linked by a smooth exponential time-dependent part for all kinds of single-well potentials. Furthermore, we argue that this result connects two distinct relevant experimental setups for trapped nanoparticles, the levitated particle in a harmonic trap, and the free particle in a box, as they are limiting cases of the general single-well potential and display the time-dependent optimal protocols. Finally, we highlight the connection between our system and an equivalent model of a gas of Brownian particles.

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  • Received 27 November 2018
  • Revised 3 March 2019

DOI:https://doi.org/10.1103/PhysRevE.99.062119

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsGeneral Physics

Authors & Affiliations

Domingos S. P. Salazar1,* and Sérgio A. Lira2,†

  • 1Unidade Acadêmica de Educacão a Distância e Tecnologia, Universidade Federal Rural de Pernambuco, Recife, Pernambuco 52171-900 Brazil
  • 2Instituto de Física, Universidade Federal de Alagoas, Maceió, Alagoas 57072-900 Brazil

  • *salazar.domingos@gmail.com
  • sergio@fis.ufal.br

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Issue

Vol. 99, Iss. 6 — June 2019

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