Postdoc @ University of Luxembourg 

Thursday June 30 – 14.45 BST

Thermodynamic consistency in open quantum systems: from exact identities to quantum master equations 

In the context of open quantum systems, a recent effort has been put in finding alternative and general derivations of master equations which do not require the secular approximation, using partial coarse graining [1] and symmetrization  techniques [2,3,4]. These generalized master equations provide an accurate dynamic description for a larger range of parameters than the standard secular Lindblad master equations. However, the question of their thermodynamic consistency has not yet been addressed. 
Here, we study the thermodynamic consistency of quantum master equations from a general point of view. Starting with a discussion of the fluctuation theorem for work, heat and entropy production at the unitary level, we derive a quantum detailed balance condition that has to be fulfilled by any time-local master equation to ensure thermodynamic consistency. While the Redfield equation breaks such conditions, we show that the validity of the latter can be restored by using secular or beyond-secular approximation schemes, already proven to be effective in restoring the positivity of the dynamical evolution [2,3,4]. 
In addition, we study the steady state for different models of master equations, proving that the breakdown of the Redfield equation at long times is strictly connected with the violation of the quantum detailed balance condition. 
We illustrate the theoretical results by a thorough numerical analysis of the paradigmatic example of a three level system. 

[1] Gernot Schaller and Tobias Brandes. Preservation of positivity by dynamical coarse graining. Phys. Rev. A, 78:022106, Aug 2008 
[2] Krzysztof Ptaszyński and Massimiliano Esposito. Thermodynamics of quantum information flows. Physical review letters, 122(15):150603, 2019. 
[3] Gavin McCauley, Benjamin Cruikshank, Denys I Bondar, and Kurt Jacobs. Accurate lindblad-form master equation for weakly damped quantum systems across all regimes. npj Quantum Information, 6(1):1–14, 2020. 
[4] Frederik Nathan and Mark S. Rudner. Universal lindblad equation for open quantum systems. Phys. Rev. B, 102:115109, Sep 2020