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Fluctuation theorems ͑FTs͒, which describe some universal properties of nonequilibrium fluctuations, are examined from a quantum perspective and derived by introducing a two-point measurement on the system. FTs for closed and open systems driven out of equilibrium by an external time-dependent force, and for open systems maintained in a nonequilibrium steady state by nonequilibrium boundary conditions, are derived from a unified approach. Applications to fermion and boson transport in quantum junctions are discussed. Quantum master equations and Green's functions techniques for computing the energy and particle statistics are presented.

We study the efficiency at maximum power, η * , of engines performing finite-time Carnot cycles between a hot and a cold reservoir at temperatures T h and Tc, respectively. For engines reaching Carnot efficiency ηC = 1 − Tc/T h in the reversible limit (long cycle time, zero dissipation), we find in the limit of low dissipation that η * is bounded from above by ηC /(2 − ηC ) and from below by ηC /2. These bounds are reached when the ratio of the dissipation during the cold and hot isothermal phases tend respectively to zero or infinity. For symmetric dissipation (ratio one) the Curzon-Ahlborn efficiency ηCA = 1 − Tc/T h is recovered.

The total entropy production of a trajectory can be split into an adiabatic and a nonadiabatic contribution, deriving, respectively, from the breaking of detailed balance via nonequilibrium boundary conditions or by external driving. We show that each of them, the total, the adiabatic, and the nonadiabatic trajectory entropy, separately satisfies a detailed fluctuation theorem.

We provide a unified thermodynamic formalism describing information transfers in autonomous as well as nonautonomous systems described by stochastic thermodynamics. We demonstrate how information is continuously generated in an auxiliary system and then transferred to a relevant system that can utilize it to fuel otherwise impossible processes. Indeed, while the joint system satisfies the second law, the entropy balance for the relevant system is modified by an information term related to the mutual information rate between the two systems. We show that many important results previously derived for nonautonomous Maxwell demons can be recovered from our formalism and use a cycle decomposition to analyze the continuous information flow in autonomous systems operating at a steady state. A model system is used to illustrate our findings.

We derive an exact (classical and quantum) expression for the entropy production of a finite system placed in contact with one or several finite reservoirs each of which is initially described by a canonical equilibrium distribution. Whereas the total entropy of system plus reservoirs is conserved, we show that the system entropy production is always positive and is a direct measure of the system-reservoir correlations and/or entanglements. Using an exactly solvable quantum model, we illustrate our novel interpretation of the Second Law in a microscopically reversible finite-size setting, with strong coupling between system and reservoirs. With this model, we also explicitly show the approach of our exact formulation to the standard description of irreversibility in the limit of a large reservoir.PACS numbers: 05.70. Ln, Starting with the groundbreaking work of Boltzmann, there have been numerous attempts to construct a microscopic derivation of the Second Law. The main difficulty is that the prime microscopic candidate for the entropy, namely, the von Neumann entropy S = −Trρ ln ρ with ρ the density matrix of the total or compound system, is a constant in time by virtue of Liouville's theorem. Related difficulties are the time-reversibility of the microscopic laws and the recurrences of the micro-states. A common way to bypass these difficulties is to introduce irreversibility in an ad hoc way, for example by reasoning that the system is in contact with idealized infinitely large heat reservoirs. Nevertheless, as was realized early on by Onsager, a consistent description of the resulting irreversible behavior still carries the undiluted imprint of the underlying time-reversibility and Liouville's theorem for the system. Examples are the symmetry of the Onsager coefficients and the fluctuation dissipation theorem. As examples of more recent discussions we cite results on work theorems and fluctuation theorems [1,2,3]. Even more relevant to the question pursued here, we cite the microscopic expression for the entropy production as the breaking, in a statistical sense, of the arrow of time [4,5,6,7,8,9,10]. We also mention that significant effort has been devoted to a detailed description and understanding of the interaction with the heat reservoirs, in particular the difficulties of dealing with the case of strong coupling [11,12].In this letter we show that the problem of entropy production can be addressed within a microscopically exact description of a finite system, without resorting to infinitely large heat reservoirs and without any assumption of weak coupling. Whereas the von Neumann entropy of system plus reservoirs is conserved, the entropy production of the system is always positive, even though it displays oscillations and recurrences typical of the finite total system. Interestingly, this entropy production is expressed in terms of the correlations and/or entanglement between system and reservoirs, so that its positivity can be explained by a corresponding negative entropy contribution contained in the...

Abstract. -The amount of work that is needed to change the state of a system in contact with a heat bath between specified initial and final nonequilibrium states is at least equal to the corresponding equilibrium free energy difference plus (resp. minus) temperature times the information of the final (resp. the initial) state relative to the corresponding equilibrium distributions.Introduction. -Szilard was the first to realize that information processing, being a physical activity, has to obey the laws of thermodynamics [1]. In particular, he showed that the entropic cost for processing one bit of information is at least k ln 2. The correct interpretation of this statement turns out to be rather subtle and the details (cost of measurement, of information storage and erasure, and of reversible and irreversible computation) have been the object of a longstanding and ongoing debate [2][3][4][5]. At the time of Szilard the transformation of information into work or vice-versa was a purely academic question. With the advent of high performance numerical simulations and the stunning developments in nano-and bio-technology, the issue has received renewed attention [6][7][8][9][10][11]. In particular, information to work transformation has been documented in computer simulations [12] and has been realized in several experiments [7,[13][14][15][16]. Furthermore, spectacular developments in statistical mechanics and thermodynamics, including the work and fluctuation theorems [8,[17][18][19][20][21][22][23] and the formulation of thermodynamics for single trajectories instead of ensemble averages [24][25][26], are very relevant in the context of information processing [12,[27][28][29][30][31].

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 investigate the efficiency of power generation by thermo-chemical engines. For strong coupling between the particle and heat flows and in the presence of a left-right symmetry in the system, we demonstrate that the efficiency at maximum power displays universality up to quadratic order in the deviation from equilibrium. A maser model is presented to illustrate our argument. The concept of Carnot efficiency is a cornerstone of thermodynamics. It states that the efficiency of a cyclic ("Carnot") thermal engine that transforms an amount Q r of energy extracted from a heat reservoir at temperature T r into an amount of work W is at most η = W/Q r ≤ η c = 1 − T l /T r , where T l is the temperature of a second, colder reservoir. The theoretical implications of this result are momentous, as they lie at the basis of the introduction by Clausius of the entropy as a state function. The practical implications are more limited, since the upper limit η c ("Carnot efficiency") is only reached for engines that operate reversibly. As a result, when the efficiency is maximal, the output power is zero. By optimizing the Carnot cycle with respect to power rather than efficiency, Curzon and Ahlborn found that the corresponding efficiency is given by η CA = 1 − T l /T r [1]. They obtained this result for a specific model, using in addition the so-called endo-reversible approximation (i.e., neglecting the dissipation in the auxiliary, work producing entity). Subsequently, the validity of this result as an upper bound, as well as its universal character, were the subject of a longstanding debate. In the regime of linear response, more precisely to linear order in η c , it was proven that the efficiency at maximum power is indeed limited by the Curzon-Ahlborn efficiency, which in this regime is exactly half of the Carnot efficiency,. The upper limit is reached for a specific class of models, namely, those for which the heat flux is strongly coupled to the work-generating flux. Interestingly, such strong coupling is also a prerequisite for open systems to achieve Carnot efficiency [3,4]. In the nonlinear regime, no general result is known. Efficiencies at maximum power, not only below but also above Curzon-Ahlborn efficiency, have been reported [5,6,7,8]. However, it was also found, again in several strong coupling models [7,8,9], that the efficiency at maximum power agrees with η CA up to quadratic order in η c , i.e., η = η c /2+η 2 c /8+O(η 3 c ), again raising the question of universality at least to this order. In this letter we prove that the coefficient 1/8 is indeed universal for strong coupling models that possess a left-right symmetry. Such a universality is remarkable in view of the fact that most explicit macroscopic relationships, for example the symmetry of Onsager coefficients, are limited to the regime of linear response. The interest in strong coupling is further motivated by the observation that it can naturally be achieved in nano-devices [10,11,12]. To complement our theoretical discussion, we also present a deta...

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