Postdoc @ Jagiellonian University, Kraków
Monday June 27 – 12.30 BST
The standard dynamical approach to quantum thermodynamics is based on Markovian master equations describing the thermalization of a system weakly coupled to a large environment. Here, based on the newly introduced notion of continuous thermomajorization, we obtain necessary and sufficient conditions for the existence of such a thermalization process transforming between given initial and final energy populations of the system. These include standard entropy production relations as a special case, but also yield a complete, continuous family of entropic functions that need to monotonically increase during the dynamics. Importantly, we significantly simplify these conditions by identifying a finitely verifiable set of constraints governing non-equilibrium transformations under master equations. What is more, the framework is also constructive, i.e., it returns an explicit set of elementary controls realizing any allowed transformation. We also present an algorithm that in a finite number of steps allows one to construct all energy distributions achievable from a given initial state via Markovian thermalization processes. The algorithm can be deployed to solve complex optimization problems in out-of-equilibrium setups and it returns explicit elementary control sequences realizing optimal transformations. We illustrate this by finding optimal protocols in the context of cooling, work extraction and catalysis. The same tools also allow one to quantitatively assess the role played by memory effects in the performance of thermodynamic protocols. We obtained exhaustive solutions on a laptop machine for systems with dimension d ≤ 7, but with heuristic methods one could access much higher d.