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Optimizing Thermodynamic Cycles with Two Finite-Sized Reservoirs

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 Added by Yu-Han Ma
 Publication date 2021
  fields Physics
and research's language is English




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We study the non-equilibrium thermodynamics of a heat engine operating between two finite-sized reservoirs with well-defined temperatures. Within the linear response regime, it is discovered that there exists a power-efficiency trade-off depending on the ratio of heat capacities ($gamma$) of the reservoirs for the engine; the uniform temperature of the two reservoirs at final time $tau$ is bounded from below by the entropy production $sigma_{mathrm{min}}propto1/tau$. We further obtain a universal efficiency at maximum power of the engine for arbitrary $gamma$. Our findings can be used to develop an optimization scenario for thermodynamic cycles with finite-sized reservoirs in practice.



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The equilibrium properties of a Janus fluid made of two-face particles confined to a one-dimensional channel are revisited. The exact Gibbs free energy for a finite number of particles $N$ is exactly derived for both quenched and annealed realizations. It is proved that the results for both classes of systems tend in the thermodynamic limit ($Ntoinfty$) to a common expression recently derived (Maestre M A G and Santos A 2020 J Stat Mech 063217). The theoretical finite-size results are particularized to the Kern--Frenkel model and confirmed by Monte Carlo simulations for quenched and (both biased and unbiased) annealed systems.
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