Estimation of parameters is a pivotal task throughout science and technology. The quantum Cramér-Rao bound provides a fundamental limit of precision allowed to be achieved under quantum theory. For closed quantum systems, it has been shown how the estimation precision depends on the underlying dynamics. Here, we propose a general formulation for metrology scenarios in open quantum systems, aiming to relate the precision more directly to properties of the underlying dynamics. This feature may be employed to enhance an estimation precision, e.g., by quantum control techniques. Specifically, we derive a Cramér-Rao bound for a fairly large class of open system dynamics, which is governed by a (time-dependent) dynamical semigroup map. We illustrate the utility of this scenario through three examples.

We provide a characterization of energy in the form of exchanged heat and work between two interacting constituents of a closed, bipartite, correlated quantum system. By defining a binding energy we derive a consistent quantum formulation of the first law of thermodynamics, in which the role of correlations becomes evident, and this formulation reduces to the standard classical picture in relevant systems. We next discuss the emergence of the second law of thermodynamics under certain—but fairly general—conditions such as the Markovian assumption. We illustrate the role of correlations and interactions in thermodynamics through two examples.

In the weak-coupling limit approach to open quantum systems, the presence of the bath is eliminated and accounted for by a master equation that introduces dissipative contributions to the system reduced dynamics: within this framework, there are no bath entropy contributions to the entropy balance. We show that, as a consequence, the entropy production fails to be positive for a class of physically legitimate, that is completely positive and trace preserving, non-Markovian dynamical maps. Moreover, in absence of the semigroup property, if the reduced dynamics has a thermal asymptotic state, this need not be stationary. Then even the integrated entropy production becomes negative. These observations imply that, when the conditions leading to reduced dynamics of semigroup type are relaxed, a consistent formulation of the second law of thermodynamics requires that the environment contribution to the entropy balance be explicitly taken into account.

A universal scheme is introduced to speed up the dynamics of a driven open quantum system along a prescribed trajectory of interest. This framework generalizes counterdiabatic driving to open quantum processes. Shortcuts to adiabaticity designed in this fashion can be implemented in two alternative physical scenarios: one characterized by the presence of balanced gain and loss, the other involves non-Markovian dynamics with time-dependent Lindblad operators. As an illustration, we engineer superadiabatic cooling, heating, and isothermal strokes for a two-level system, and provide a protocol for the fast thermalization of a quantum oscillator.