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

Chakrabarti, Rajarshi (2009) Transient state work fluctuation theorem for a classical harmonic oscillator linearly coupled to a harmonic bath. In: Pramana, 72 (4). pp. 665-677.

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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.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Springer India and Indian Academy of Sciences.
Keywords: Fluctuation theorems;classical dissipative system;system plus bath coupling
Department/Centre: Division of Chemical Sciences > Inorganic & Physical Chemistry
Date Deposited: 14 Dec 2009 09:31
Last Modified: 19 Sep 2010 05:33
URI: http://eprints.iisc.ernet.in/id/eprint/20539

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