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note
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The approach of van Zon and Cohen to the calculation of P (Q, t) is based on the integration of a work distribution function, P (W, t), over all values of W under an energy conservation (first law) constraint. P (W, t) is a Gaussian when v, the speed of the trap, is nonzero. However, when v = 0 (the limit of interest for our calculations), no work is done, and the work distribution is a delta function, δ (W). Integration over W now merely equates Q to the net energy change, without determining its distribution at all; an average over the stochastic trajectories of the particle and its initial distribution must be carried out to obtain P (Q, t).
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on the thermodynamics of a colloidal particle trapped in a bistable potential and modulated by an external periodic force, exact heat and work distributions were calculated, but only by numerical solution of a Fokker-Plank equation, followed by numerical inversion of a Fourier transform; closed-form expressions were not derived. Fluctuations in the heat and work were also probed in a study by [10.1103/PhysRevLett.96.070603on the dynamics of a colloidal particle trapped in a time-dependent nonharmonic potential, but no closed-form expressions for the associated heat distribution were derived here either.
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on the thermodynamics of a colloidal particle trapped in a bistable potential and modulated by an external periodic force, exact heat and work distributions were calculated, but only by numerical solution of a Fokker-Plank equation, followed by numerical inversion of a Fourier transform; closed-form expressions were not derived. Fluctuations in the heat and work were also probed in a study by V. Blickle, T. Speck, L. Helden, U. Seifert, and C. Bechinger [Phys. Rev. Lett. 96, 070603 (2006)] 10.1103/PhysRevLett.96.070603
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68949122330
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The definition of the heat in Eq. corrects a typographical error in Eq. of one of our earlier papers on the subject [, 10.1103/PhysRevE.80.011118; all the calculations in that paper were carried out using the correct definition of Q (t).
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The definition of the heat in Eq. corrects a typographical error in Eq. of one of our earlier papers on the subject [D. Chatterjee and B. J. Cherayil, Phys. Rev. E 80, 011118 (2009)] 10.1103/PhysRevE.80.011118
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