Abstract
Optimal (reversible) processes in thermodynamics can be modelled as step-by-step processes, where the system is successively thermalized with respect to different Hamiltonians by an external thermal bath. However, in practice interactions between system and thermal bath will take finite time, and precise control of their interaction is usually out of reach. Motivated by this observation, we consider finite-time and uncontrolled operations between system and bath, which result in thermalizations that are only partial in each step. We show that optimal processes can still be achieved for any non-trivial partial thermalizations at the price of increasing the number of operations, and characterise the corresponding tradeoff. We focus on work extraction protocols and show our results in two different frameworks: A collision model and a model where the Hamiltonian of the working system is controlled over time and the system can be brought into contact with a heat bath. Our results show that optimal processes are robust to noise and imperfections in small quantum systems, and can be achieved by a large set of interactions between system and bath.
Highlights
Recent years have experienced a renewed interest in understanding thermodynamics in the quantum regime [1, 2]
We focus on work extraction protocols and show our results in two different frameworks: A collision model and a model where the Hamiltonian of the working system is controlled over time and the system can be brought into contact with a heat bath
In this work we have considered thermodynamic processes in which contacts between S and B correspond to imperfect thermalizations, which capture large classes of possible error models or finite-time equilibration processes
Summary
Recent years have experienced a renewed interest in understanding thermodynamics in the quantum regime [1, 2]. A common assumption in the field is that a system thermalizes to a Gibbs state when put in contact with a thermal bath. While this is perfectly reasonable, it requires some implicit assumptions: For exam-. We consider discrete processes consisting of N small steps following a smooth curve between two fixed points in parameter space, where the system interacts for a certain time tth with the thermal bath at each step. Let us introduce a parameter α, such that for α = 1, there is no interaction, and for α = 0 the system thermalizes perfectly in each step. Α = α(tth) is a function of the interaction time with the bath in each step.
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