Graph theory analysis of open quantum systems: classical simulation of quantumcoherent thermal machines
Last updated November 29, 2018 by Alessandro Ferraro
Wednesday, Nov 28th 2018, 04:00 PM, MAPTC/0G/006
Speaker: Javier Onam Gonzalez (University of La Laguna).
Abstract:
Graph theory has proved to be a powerful tool for characterizing nonequilibrium steady states of balance equations [1]. A nonvanishing entropy production rate can always be associated with such kind of stationary states. There are many different ways to decompose this thermodynamic quantity into several contributions, each of them related to one or more graph objects. Interestingly, there exists a particular choice, the Hill’s decomposition [2], for which every single contribution satisfies the second law of thermodynamics. Most importantly, each term in the Hill decomposition is directly linked with a graph object usually called circuit. We extend this circuit decomposition to study quantum implementations of absorption devices [3]. Namely, we address three issues:
(i) The thermodynamically consistent definitions of the circuit heat currents. These magnitudes facilitates the search for bounds on the device performance. (ii) Thermodynamic mechanism behind each circuit and sources of irreversibility. (iii) Relation between topology and currents when scaling up absorption devices.
Additionally, we discuss the importance of this graph theory approach for a consistent definition of ‘classicality’ in quantum thermodynamics [4].
[1] Rev. Mod. Phys. 48, 571 (1976) [2] J. Theoret. Biol. 10, 442459 (1966) [3] New J. Phys. 19 113037 (2017) [4] arXiv: 1810.04174

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