We expand the standard thermodynamic framework of a system coupled to a thermal reservoir by considering a stream of independently prepared units repeatedly put into contact with the system. These units can be in any nonequilibrium state and interact with the system with an arbitrary strength and duration. We show that this stream constitutes an effective resource of nonequilibrium free energy and identify the conditions under which it behaves as a heat, work or information reservoir. We also show that this setup provides a natural framework to analyze information erasure ("Landauer's principle") and feedback controlled systems ("Maxwell's demon"). In the limit of a short system-unit interaction time, we further demonstrate that this setup can be used to provide a thermodynamically sound interpretation to many effective master equations. We discuss how nonautonomously driven systems, micromasers, lasing without inversion, and the electronic Maxwell demon, can be thermodynamically analyzed within our framework. While the present framework accounts for quantum features (e.g. squeezing, entanglement, coherence), we also show that quantum resources do not offer any advantage compared to classical ones in terms of the maximum extractable work.

We present a physical implementation of a Maxwell demon which consists of a conventional single electron transistor (SET) capacitively coupled to another quantum dot detecting its state. Altogether, the system is described by stochastic thermodynamics. We identify the regime where the energetics of the SET is not affected by the detection, but where its coarse-grained entropy production is shown to contain a new contribution compared to the isolated SET. This additional contribution can be identified as the information flow generated by the ''Maxwell demon'' feedback in an idealized limit.

We propose a method to study the thermodynamic behaviour of small systems beyond the weak coupling and Markovian approximation, which is different in spirit from conventional approaches. The idea is to redefine the system and environment such that the effective, redefined system is again coupled weakly to Markovian residual baths and thus, allows to derive a consistent thermodynamic framework for this new system-environment partition. To achieve this goal we make use of the reaction coordinate (RC) mapping, which is a general method in the sense that it can be applied to an arbitrary (quantum or classical and even time-dependent) system coupled linearly to an arbitrary number of harmonic oscillator reservoirs. The core of the method relies on an appropriate identification of a part of the environment (the RC), which is subsequently included as a part of the system. We demonstrate the power of this concept by showing that non-Markovian effects can significantly enhance the steady state efficiency of a three-level-maser heat engine, even in the regime of weak system-bath coupling. Furthermore, we show for a single electron transistor coupled to vibrations that our method allows one to justify master equations derived in a polaron transformed reference frame.can then be shown to have a transparent thermodynamic interpretation [3-5] and they provide the work horse for the field of quantum and stochastic thermodynamics, see [6][7][8][9][10] for recent reviews.However, many interesting physical effects cannot be captured with such a ME approach and thus, quantum and stochastic thermodynamics is still restricted to a small regime of applicability. Consequently, many groups have started to look at thermodynamics in the strong coupling and non-Markovian regime . Though these works present important theoretical cornerstones, they are still far away from providing a satisfactory extension of thermodynamics beyond the weak coupling limit. In particular, if one wishes to address the performance of a steadily working heat engine, the general results derived in [11][12][13][14][15][16][17][18][19][20][21] are not of great help because they either focus on integrated changes of thermodynamic values (e.g., the total heat exchanged in a finite time instead of the rate of heat exchange) and additionally rely on an initially decorrelated system-environment state [11][12][13] and/or coupling only to a single thermal reservoir [11,[13][14][15][16][17];or they remain very formal [18][19][20][21]. Furthermore, model-specific studies are either based on simple or exactly solvable models from the field of quantum transport [22][23][24][25] and quantum Brownian motion [26][27][28][29], or spin-boson models [30][31][32] often in combination with specific transformations applicable only to special Hamiltonians (polaron transformations) [31,[33][34][35][36]; or the investigations are restricted to numerical studies [37].The goal of this paper is to close the gap between the general results, which are often hard to apply in practice, and studi...

We establish a theoretical method which goes beyond the weak-coupling and Markovian approximations while remaining intuitive, using a quantum master equation in a larger Hilbert space. The method is applicable to all impurity Hamiltonians tunnel coupled to one (or multiple) baths of free fermions. The accuracy of the method is in principle not limited by the system-bath coupling strength, but rather by the shape of the spectral density and it is especially suited to study situations far away from the wide-band limit. In analogy to the bosonic case, we call it the fermionic reaction coordinate mapping. As an application, we consider a thermoelectric device made of two Coulomb-coupled quantum dots. We pay particular attention to the regime where this device operates as an autonomous Maxwell demon shoveling electrons against the voltage bias thanks to information. Contrary to previous studies, we do not rely on a Markovian weak-coupling description. Our numerical findings reveal that in the regime of strong coupling and non-Markovianity, the Maxwell demon is often doomed to disappear except in a narrow parameter regime of small power output.

We consider a classical and possibly driven composite system X ⊗ Y weakly coupled to a Markovian thermal reservoir R so that an unambiguous stochastic thermodynamics ensues for X ⊗ Y . This setup can be equivalently seen as a system X strongly coupled to a non-Markovian reservoir Y ⊗ R. We demonstrate that only in the limit where the dynamics of Y is much faster than X, our unambiguous expressions for thermodynamic quantities, such as heat, entropy, or internal energy, are equivalent to the strong coupling expressions recently obtained in the literature using the Hamiltonian of mean force. By doing so, we also significantly extend these results by formulating them at the level of instantaneous rates and by allowing for time-dependent couplings between X and its environment. Away from the limit where Y evolves much faster than X, previous approaches fail to reproduce the correct results from the original unambiguous formulation, as we illustrate numerically for an underdamped Brownian particle coupled strongly to a non-Markovian reservoir.