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arXiv:1801.09187 · Journal of Mathematical Physics

A model of Josephson junctions on Boson systems—Currents and entropy production rate

Tomohiro Kanda

Published Oct 1, 2018• 2 citations
arXivHTMLPDF

Abstract

Non-equilibrium steady states, in the sense of Ruelle [Commun. Math. Phys. 224, 3–16 (2001)], of Boson systems with Bose–Einstein condensation are investigated with the aid of the C*-algebraic method. The model consists of a quantum particle and several bosonic reservoirs. We show that the mean entropy production rate is strictly positive and independent of phase differences provided that the temperatures or the chemical potentials of reservoirs are different. Moreover, Josephson currents occur without entropy production, if the temperatures and the chemical potentials of reservoirs are identical.

DOI
10.1063/1.5025598

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Non-equilibrium steady states, in the sense of Ruelle [Commun. Math. Phys. 224, 3–16 (2001)], of Boson systems with Bose–Einstein condensation are investigated with the aid of the C*-algebraic method. The model consists of a quantum particle and several bosonic reservoirs. We show that the mean entropy production rate is strictly positive and independent of phase differences provided that the temperatures or the chemical potentials of reservoirs are different. Moreover, Josephson currents occur without entropy production, if the temperatures and the chemical potentials of reservoirs are identical.
Non-equilibrium steady states (NESS) of Boson systems with different phases are investigated with the aid of the C^*-algebraic method. The system consists of sample and several free or pure-hopping bosonic reservoirs coupled with each other. Initially, the sample and reservoirs are uncoupled and in equilibrium with temperatures, local densities, and phases. At t=0, the reservoirs couple with each other through the sample. NESS are constructed as time limit of the composition of initial state and time evolution of coupled system. In NESS, Josephson currents and the mean entropy production rates are calculated. The mean entropy production rate does not depend on phase differences. As consequence, the currents provided to phase differences produces no entropy.
We consider the generic model of a finite-size quantum electron system connected to two (temperature and particle) reservoirs. The quantum open system is driven out of equilibrium by the presence of both potential temperature and chemical differences between the two reservoirs. The nonequilibrium (NE) thermodynamical properties of such a quantum open system are studied for the steady state regime. In such a regime, the corresponding NE density matrix is built on the so-called generalised Gibbs ensembles. From different expressions of the NE density matrix, we can identify the terms related to the entropy production in the system. We show, for a simple model, that the entropy production rate is always a positive quantity. Alternative expressions for the entropy production are also obtained from the Gibbs–von Neumann conventional formula and discussed in detail. Our results corroborate and expand earlier works found in the literature.
Nonequilibrium steady-state currents, unlike their equilibrium counterparts, continuously dissipate energy into their physical surroundings leading to entropy production and time-reversal symmetry breaking. This Letter discusses these issues in the context of quantum impurity models. We use simple thermodynamic arguments to define the rate of entropy production sigma and show that sigma has a simple information-theoretic interpretation in terms of nonequilibrium distribution functions. This allows us to show that the entropy production is strictly positive for any nonequilibrium steady state. We conclude by applying these ideas to the resonance level model and the Kondo model.
By making use of a recently proposed framework for the inference of thermodynamic irreversibility in bosonic quantum systems, we experimentally measure and characterize the entropy production rates in the nonequilibrium steady state of two different physical systems-a micromechanical resonator and a Bose-Einstein condensate-each coupled to a high finesse cavity and hence also subject to optical loss. Key features of our setups, such as the cooling of the mechanical resonator and signatures of a structural quantum phase transition in the condensate, are reflected in the entropy production rates. Our work demonstrates the possibility to explore irreversibility in driven mesoscopic quantum systems and paves the way to a systematic experimental assessment of entropy production beyond the microscopic limit.