Postdoc @ Lund University

Friday July 1 – 9.45 BST

##### Extractable work in a Szilard engine with a finite-size reservoir

The Szilard engine is a paradigmatic protocol in thermodynamics when it comes to the question of how much work can be extracted from a system coupled to a single thermal reservoir, by means of performing measurement and feedback. Originally conceived as a thought experiment by Szilard [1], experimental realizations of the engine have been implemented over the last few years, for example in the context of nanodevices such as quantum dots [2,3]. In an ideal Szilard engine, in which the system is coupled to an infinite-size bath at constant temperature, the extractable work has an upper bound, reaching k_BT ln 2 for a quasi-static, large amplitude cycle.

Here, we aim to study how the extraction of work in a Szilard engine is impacted by finite-size reservoirs. We focus on a system constituted of a quantum dot, which is, in turn, coupled to a finite-size fermionic reservoir. Due to the exchange of heat between the quantum dot and the reservoir, the temperature of the reservoir develops fluctuations in time. We find that the maximum amount of work that can be extracted is always lower than in the ideal Szilard engine, with infinite size reservoirs. Moreover, in the limit of large but finite-size reservoirs, the difference in extractable work is inversely proportional to the heat capacity of the reservoir.

Moreover, we compare our results with previously derived upper bounds for the extractable work derived for finite-size reservoirs [4,5], and show that our results are consistent with these bounds.

[1] L. Szilard. Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen, Z. Physik 53, 840–856 (1929).

[2] J. V. Koski, V. F. Maisi, J. P. Pekola and D. V. Averin. Experimental realization of a Szilard engine with a single electron, Proc Natl Acad Sci 11, 13786 (2014).

[3] D. Barker, M. Scandi, S. Lehmann, C. Thelander, K. A. Dick, M. Perarnau-Llobet, and V. F. Maisi. Experimental Verification of the Work Fluctuation-Dissipation Relation for Information-to-Work Conversion, Phys. Rev. Lett. 128, 040602 (2022).

[4] R. Clausius. Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie, Ann. Phys. 201, 353 (1865).

[5] P. Strasberg and A. Winter. First and second law of quantum thermodynamics: A consistent derivation based on a microscopic definition of entropy. PRX Quantum 2, 030202 (2021).