• Transient state work fluctuation theorem for a classical harmonic oscillator linearly coupled to a harmonic bath

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      https://www.ias.ac.in/article/fulltext/pram/072/04/0665-0677

    • Keywords

       

      Fluctuation theorems; classical dissipative system; system plus bath coupling.

    • Abstract

       

      Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.

    • Author Affiliations

       

      Rajarshi Chakrabarti1 2

      1. Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560 012, India
      2. Department of Materials Science and Engineering, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801, USA
    • Dates

       
  • Pramana – Journal of Physics | News

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