Master equations of Lindblad type have attained prominent status in the fields of quantum optics and quantum information since they are guaranteed to satisfy fundamental notions of quantum dynamics such as complete positivity. When Lindblad operators are used to describe thermal reservoirs in contact with an open quantum system, the fundamental laws of thermodynamics and the fluctuation‐dissipation theorem provide additional mandatory criteria. We show several examples of innocent‐looking Lindblad operators which have questionable properties in this regard. Compatibility criteria between Hamiltonian and Lindblad terms as well as consequences of their violation are discussed. An alternative stochastic approach to dissipative quantum dynamics is outlined and illustrated through a harmonic‐chain model for which the approach of local Lindblad operators fails.

Within the emerging field of quantum thermodynamics the issues of heat transfer and heat rectification are basic ingredients for the understanding and design of heat engines or refrigerators at nanoscales. Here, a consistent and versatile approach for mesoscopic devices operating with continuous degrees of freedom is developed valid from low up to strong system-reservoir couplings and over the whole temperature range. It allows to cover weak to moderate nonlinearities and is applicable to various scenarios including the presence of disorder and external time-dependent fields. As a particular application coherent one-dimensional chains of anharmonic oscillators terminated by thermal reservoirs are analyzed with particular focus on rectification. The efficiency of the method opens a door to treat also rather long chains and extensions to higher dimensions and geometries.

Recently, it has been shown that entropy can be used to sort Brownian particles according to their size. In particular, a combination of a static and a time-dependent force applied on differently sized particles which are confined in an asymmetric periodic structure can be used to separate them efficiently, by forcing them to move in opposite directions. In this paper, we investigate the optimization of the performance of the "entropic splitter". Specifically, the splitting mechanism and how it depends on the geometry of the channel, and the frequency and strength of the periodic forcing is analyzed. Using numerical simulations, we demonstrate that a very efficient and fast separation with a practically 100% purity can be achieved by a proper optimization of the control variables. The results of this work could be useful for a more efficient separation of dispersed phases such as DNA fragments or colloids dependent on their size.

Heat transport in open quantum systems is particularly susceptible to the modeling of systemreservoir interactions. It thus requires us to consistently treat the coupling between a quantum system and its environment. While perturbative approaches are successfully used in fields like quantum optics and quantum information, they reveal deficiencies-typically in the context of thermodynamics, when it is essential to respect additional criteria such as fluctuation-dissipation theorems. We use a non-perturbative approach for quantum dissipative dynamics based on a stochastic Liouville-von Neumann equation to provide a very general and extremely efficient formalism for heat currents and their correlations in open harmonic chains. Specific results are derived not only for firstbut also for second-order moments, which requires us to account for both real and imaginary parts of bath-bath correlation functions. Spatiotemporal patterns are compared with weak coupling calculations. The regime of stronger system-reservoir couplings gives rise to an intimate interplay between reservoir fluctuations and heat transfer far from equilibrium.

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