Graph theory analysis of open quantum systems: classical simulation of quantum-coherent 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).

Graph theory has proved to be a powerful tool for characterizing non-equilibrium
steady states of balance equations [1]. A non-vanishing 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, 442-459 (1966)
[3] New J. Phys. 19 113037 (2017)
[4] arXiv: 1810.04174


We are a Research Cluster of the School of Mathematics and Physics at Queen’s University Belfast in Northern Ireland. Our research interests are focused primarily on computational and theoretical physics.

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