Optimal work of the quantum Szilard engine under isothermal processes with inevitable irreversibility

Abstract

We have found the optimal conditions for work performed by the quantum Szilard engine (SZE) containing multi-particles under isothermal processes with inevitable irreversibility. We define the restorability as the probability that the reversibility of an engine with inevitable irreversibility is achieved when the time-backward process is performed. The optimal condition is then obtained when the restorability is maximized. This is equivalent to the condition that the time-forward force is equal to the time-backward force. We numerically confirm our expectation by using the quantum SZE containing three bosons or fermions.

Quantum heat engine based on level degeneracy

“…Our analysis shows an effective way of converting lack of information, emerging from degeneracy of energy levels, to useful work without any measurement but using two different reservoirs. The amount of extractable work depends on the nature of the particle such as distinguishable particles, bosons, or fermions [9,21,22,24,[26][27][28][29]. The cycle we use is quite similar to the Stirling cycle.…”

Quantum Szilard Engine with Attractively Interacting Bosons

“…Without interactions, two bosons yield a higher work output than two fermions or classical particles [25]. Different facets of the quantum Szilard engine have been studied, including optimization of the cycle [26,27] or the effect of spin [28] and parity [29], but all for noninteracting particles. Interactions have so far only been discussed for two attractive bosons [30], where an increased work output was attributed to a classical effect.…”

“…However, for N ≥ 2, this does not hold any longer; e.g., there are no removal positions l rem 1 satisfying p 1 ðl rem 1 Þ ¼ 1 due to the finite probability of fluctuations in particle number. Similar to the noninteracting case [27], we choose the optimal l rem n , maximizing p n ðl rem n Þ. We note that the extracted work for N ≥ 2 at finite temperature is lower than the theoretical bound to the information gain k B TI.…”

Bosonic Szilard engine assisted by Feshbach resonances

“…A highly interesting question is, how thermodynamic properties are changed when quantum effects are taken into account. Different quantum versions of Szilard's engine have been suggested, with single-particle [10] to many-body working media [11][12][13][14][15][16][17][18]. For engines with non-interacting particles, bosons were found superior to fermions [11].…”