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We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths beyond perturbation theory. Our approach is based on the exact time-local quantum master equation for the reduced open…
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…
Surprisingly the looking natural random walk leading to Brownian motion occurs to be often biased in a very subtle way: usually refers to only approximate fulfillment of thermodynamical principles like maximizing uncertainty. Recently, a…
Quantum technology is progressing towards fast quantum control over systems interacting with small environments. Hence such technologies are operating in a regime where the environment remembers the system's past, and the applicability of…
Recent understanding of the thermodynamics of small-scale systems have enabled the characterization of the thermodynamic requirements of implementing quantum processes for fixed input states. Here, we extend these results to construct…
If the von Neumann equation is modified by time dependent statistical weights, the time rate of entropy, the entropy exchange and production of a Schottky system are derived whose Hamiltonian does not contain the interaction with the…
We present a framework for efficient extraction of the viscosity solutions of nonlinear Hamilton-Jacobi equations with convex Hamiltonians. These viscosity solutions play a central role in areas such as front propagation, mean-field games,…
Optimization of cyclic stochastic heat engines, a topic spanning decades of research, commonly assumes fixed control or response parameters at discrete points in the cycle-a limitation that often leads to experimentally impractical…
The total entropy production of stochastic systems can be divided into three quantities. The first corresponds to the excess heat, whilst the second two comprise the house-keeping heat. We denote these two components the transient and…
The main goal of this paper is to extend and apply the principle of maximum entropy (MaxEnt) to incomplete quantum process estimation tasks. We will define a so-called process entropy function being the von Neumann entropy of the state…
We discuss fundamental features of the local expression for the entropy production rate of the nonequilibrium quantum dynamics of open systems and its relations to memory effects and the spectrum of the generator of the dynamics. Defining…
For two canonical examples of driven mesoscopic systems - a harmonically-trapped Brownian particle and a quantum dot - we numerically determine the finite-time protocols that optimize the compromise between the standard deviation and the…
Various engine types are thermodynamically equivalent in the quantum limit of small 'engine action'. Our previous derivation of the equivalence is restricted to Markovian heat baths and to implicit classical work repository (e.g., laser…
In this paper, we identify a class of time-varying port-Hamiltonian systems that is suitable for studying problems at the intersection of statistical mechanics and control of physical systems. Those port-Hamiltonian systems are able to…
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…
Describing open quantum systems far from equilibrium is challenging, in particular when the environment is mesoscopic, when it develops nonequilibrium features during the evolution, or when the memory effects cannot be disregarded. Here, we…
It is supposed that the exponential multiplier in the method of the non-equilibrium statistical operator (Zubarev`s approach) can be considered as a distribution density of the past lifetime of the system, and can be replaced by an…
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics like work, heat and entropy production to the level of individual trajectories of well-defined…
The resource-theoretic approach to quantum thermodynamics assumes complete knowledge of the thermal equilibrium against which thermodynamic resources are defined. In practice, however, this state is determined by the system Hamiltonian and…
We derive statistical-mechanical speed limits on dissipation from the classical, chaotic dynamics of many-particle systems. In one, the rate of irreversible entropy production in the environment is the maximum speed of a deterministic…