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• Sørdal, Vegard Børve & Bergli, Joakim (2019). Deep reinforcement learning for quantum Szilard engine optimization. Physical Review A (PRA). ISSN 2469-9926. 100(4). doi: 10.1103/PhysRevA.100.042314. Full text in Research Archive Show summary

  Machine learning techniques based on artificial neural networks have been successfully applied to solve many problems in science. One of the most interesting domains of machine learning, reinforcement learning, has a natural applicability for optimization problems in physics. In this paper, we use deep reinforcement learning and chopped random basis optimization to solve an optimization problem based on the insertion of an off-center barrier in a quantum Szilard engine. We show that by using designed protocols for the time dependence of the barrier strength, we can achieve an equal splitting of the wave function (1/2 probability to find the particle on either side of the barrier) even for an asymmetric Szilard engine in such a way that no information is lost when measuring which side the particle is found. This implies that the asymmetric nonadiabatic Szilard engine can operate with the same efficiency as the traditional Szilard engine with adiabatic insertion of a central barrier. We compare the two optimization methods and demonstrate the advantage of reinforcement learning when it comes to constructing robust and noise-resistant protocols.

• Sørdal, Vegard Børve & Bergli, Joakim (2019). Quantum particle in a split box: Excitations to the ground state. Physical Review A (PRA). ISSN 2469-9926. 99(2), p. 1–6. doi: 10.1103/PhysRevA.99.022121. Full text in Research Archive Show summary

  We discuss two different approaches for splitting the wave function of a single-particle box (SPB) into two equal parts. Adiabatic insertion of a barrier in the center of a SPB in order to make two compartments which each have probability 1/2 of finding the particle in it is one of the key steps for a Szilard engine. However, any asymmetry between the volume of the compartments due to an off-center insertion of the barrier results in a particle that is fully localized in the larger compartment, in the adiabatic limit. We show that rather than exactly splitting the eigenfunctions in half by a symmetric barrier, one can use a nonadiabatic insertion of an asymmetric barrier to induce excitations to only the first excited state of the full box. As the barrier strength goes to infinity the excited state of the full box becomes the ground state of one of the new boxes. Thus, we can achieve close to exact splitting of the probability between the two compartments using the more realistic nonadiabatic, not perfectly centered barrier, rather than the idealized adiabatic and central barrier normally assumed.

• Sørdal, Vegard Børve; Bergli, Joakim & Galperin, Yuri (2017). Influence of measurement error on Maxwell's demon. Physical Review E (PRE). ISSN 2470-0045. 95(6). doi: 10.1103/PhysRevE.95.062129. Full text in Research Archive Show summary

  In any general cycle of measurement, feedback, and erasure, the measurement will reduce the entropy of the system when information about the state is obtained, while erasure, according to Landauer's principle, is accompanied by a corresponding increase in entropy due to the compression of logical and physical phase space. The total process can in principle be fully reversible. A measurement error reduces the information obtained and the entropy decrease in the system. The erasure still gives the same increase in entropy, and the total process is irreversible. Another consequence of measurement error is that a bad feedback is applied, which further increases the entropy production if the proper protocol adapted to the expected error rate is not applied. We consider the effect of measurement error on a realistic single-electron box Szilard engine, and we find the optimal protocol for the cycle as a function of the desired power P and error ɛ.

• Sørdal, Vegard Børve; Bergli, Joakim & Galperin, Yuri (2016). Cooling by heating: Restoration of the third law of thermodynamics. Physical Review E (PRE). ISSN 2470-0045. 93(3). doi: 10.1103/PhysRevE.93.032102. Full text in Research Archive Show summary

  We have made a simple and natural modification of a recent quantum refrigerator model presented by Cleuren et al. [Phys. Rev. Lett. 108, 120603 (2012)]. The original model consist of two metal leads acting as heat baths and a set of quantum dots that allow for electron transport between the baths. It was shown to violate the dynamic third law of thermodynamics (the unattainability principle, which states that cooling to absolute zero in finite time is impossible). By taking into consideration the finite energy level spacing Δ, in metals we restore the third law while keeping all of the original model's thermodynamic properties intact down to the limit of kBT∼Δ, where the cooling rate is quenched. The spacing Δ depends on the confinement of the electrons in the lead and therefore, according to our result larger samples (with smaller level spacing), could be cooled efficiently to lower absolute temperatures than smaller ones. However, a large lead makes the assumption of instant equilibration of electrons implausible; in reality one would only cool a small part of the sample and we would have a nonequilibrium situation. This property is expected to be model independent and raises the question whether we can find an optimal size for the lead that is to be cooled. ©2016 American Physical Society

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• Galperin, Yuri; Bergli, Joakim & Sørdal, Vegard Børve (2018). Optimal protocols for a Maxwell Demon device with errors. Full text in Research Archive
• Sørdal, Vegard Børve (2019). Entropy production and informasjon processing in stochastic thermodynamics. Det matematisk-naturvitenskapelige fakultet. Full text in Research Archive

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