We study the thermodynamic efficiency of a nanosized photoelectric device and show that at maximum power output, the efficiency is bounded from above by a result closely related to the Curzon-Ahlborn efficiency. We find that this upper bound can be attained in nanosized devices displaying strong coupling between the generated electron flux and the incoming photon flux from the sun. DOI: 10.1103/PhysRevB.80.235122 PACS number͑s͒: 05.70.Ln, 05.30.Ϫd, 73.50.Pz Understanding and controlling the mechanisms that determine the efficiency of photoelectric devices is of fundamental importance in the quest for efficient and clean sources of energy. Thermodynamically speaking, these devices are driven by the temperature difference between a hot reservoir ͑sun, temperature T s ͒ and a cold reservoir ͑earth, ambient temperature T͒. Therefore, like any heat engine, the efficiency at which the conversion of radiation into electrical energy takes place has a universal upper bound given by the Carnot efficiency ͑1͒Although this result has fundamental theoretical implications, it is of poor practical use since it is only reached when the device is operating under reversible conditions. Hence the generated power, defined as the output energy divided by the ͑infinite͒ operation time, goes to zero. In realistic circumstances of finite power output, the efficiency will necessarily be below the Carnot limit due to irreversible processes taking place in the device. Another source of possible efficiency decrease are energy losses within the device for example due to nonradiative recombination of charge carriers. Since the operational parameters of the device are mostly determined in such a way that a maximum power output is obtained, Curzon and Ahlborn examined in 1975 the efficiency of a Carnot cycle with a finite cycling time and, using the endoreversible approximation, found an efficiency at maximum2 This result is remarkable since it does not depend on the specific details of the system, and thus the question of universality naturally arises. Recent works [3][4][5][6][7] have indeed demonstrated that in the linear regime ͑small temperature differences, c Ӷ 1͒ the Curzon-Ahlborn efficiency is universal for so-called strongly coupled systems, where the heat and work producing fluxes are proportional. In these systems internal energy losses are absent, implying that the resulting efficiency is exclusively determined by the ͑unavoidable͒ irreversible processes occurring at finite power. Hence, at least in the linear regime, the CurzonAhlborn efficiency is indeed a universal upper bound, with a similar status as the Carnot efficiency. In the nonlinear regime, the efficiency at maximum power becomes device dependent but is again found to be highest for strongly coupled systems. Remarkably, it remains closely related to the Curzon-Ahlborn result. 6,7 While energy losses are almost unavoidable in the macroscopic world, new technological developments at the nanoscale open up the road to highly efficient devices. In thermoelectric researc...

Biological electron transport is classically thought to occur over nanometre distances, yet recent studies suggest that electrical currents can run along centimetre-long cable bacteria. The phenomenon remains elusive, however, as currents have not been directly measured, nor have the conductive structures been identified. Here we demonstrate that cable bacteria conduct electrons over centimetre distances via highly conductive fibres embedded in the cell envelope. Direct electrode measurements reveal nanoampere currents in intact filaments up to 10.1 mm long (>2000 adjacent cells). A network of parallel periplasmic fibres displays a high conductivity (up to 79 S cm−1), explaining currents measured through intact filaments. Conductance rapidly declines upon exposure to air, but remains stable under vacuum, demonstrating that charge transfer is electronic rather than ionic. Our finding of a biological structure that efficiently guides electrical currents over long distances greatly expands the paradigm of biological charge transport and could enable new bio-electronic applications.

In a recent letter, Cleuren et. al. [1] proposed a mechanism for solar refrigeration composed of two metallic leads mediated by two coupled quantum dots and powered by (solar) photons. In their analysis the refrigerator can operate to T r → 0 and the cooling flux ˙ Q r ∝ T r. We comment that this model violates the dynamical version of the III-law of thermodynamics. There are seemingly two independent formulation of the third law. The first, known as the Nernst heat theorem, implies that the entropy flow from any substance at absolute zero temperature is zero. At steady state the second law implies that the total entropy production is non-negative, i − ˙ Qi Ti ≥ 0 where ˙ Q i is positive for heat flowing into the system from the i-th bath. In order to insure the fulfillment of the second law when one of the heat baths (labeled k) approaches the absolute zero temperature. It is necessary that the entropy production from this bath scales as ˙ S k ∼ T α k with α ≥ 0. For the case where α = 0 the fulfillment of the second law depends on the entropy production of the other baths, which should compensate on the negative entropy production of the k bath. The first formulation of the third law slightly modifies this restriction. Instead of α ≥ 0 the third low impose α > 0 guaranteeing that at the absolute zero ˙ S k = 0. The second formulation of the third law is a dynamical one, known as the unatinability principle: No refrigerator can cool a system to absolute zero temperature at finite time. This formulation is more restrictive, imposing limitations on the spectral density and the dispersion dynamics of the heat bath [2]. We quantify this formulation by evaluating the characteristic exponent ζ of the cooling process dT (t) dt ∼ −T ζ , T → 0 (1) Namely for ζ < 1 the system is cooled to zero temperature at finite time. Eq.(1) can be related to the heat flow: ˙ Q k (T k (t)) = −c V (T k (t)) dT k (t) dt (2) where c V is the heat capacity of the bath. The refrigerator presented in [1] violates the III-law as in Eqs. (2) and (1). For an electron reservoir at low temperature the heat capacity c V ∼ T. The heat current of the refrigerator of [1] ˙ Q r ∝ T r therefore one obtains ζ = 0 hence zero temperature is achieved at finite time, in contradiction with the third law. Finding the flow in the analysis of [1] is not a trivial task. A possible explanation emerges from the assumption in [1] that transitions between lower and higher levels within the individual dots are negligible. Photon assisted tunneling between dots produce a week tunnel current [3]. In comparison quenching transitions in the individual dots cannot be neglected. A modified master equation which includes these transitions can be constructed for a five level system: ˙ p = M · p where p = (p 0 , p ld , p rd , p lu , p ru) T. Where p 0 is the probability of finding no electron in the double dot and p ij is the probability of finding one electron in the corresponding energy level, with l-left, r-right, d-down, u-up. The M matrix is 5x5 matrix which includes al...

We derive general relations between maximum power, maximum efficiency, and minimum dissipation regimes from linear irreversible thermodynamics. The relations simplify further in the presence of a particular symmetry of the Onsager matrix, which can be derived from detailed balance. The results are illustrated on a periodically driven system and a three terminal device subject to an external magnetic field.

We elucidate the connection between various fluctuation theorems by a microcanonical version of the Crooks relation. We derive the microscopically exact expression for the work distribution in an idealized Joule experiment, namely for an object, convex but otherwise of arbitrary shape, moving at constant speed through an ideal gas. Analytic results are compared with molecular dynamics simulations of a hard disk gas.PACS numbers: 05.70. Ln, Microscopic time-reversibility implies, in a system at equilibrium, the basic symmetry of detailed balance, stating that any process and its time reverse occur equally frequently. In the linear regime outside equilibrium this property entails, as Onsager has first shown, a relation between fluctuation and dissipation, since in this regime one cannot distinguish between the average regression following an external perturbation or an equilibrium fluctuation. Over the past decade, time-reversibility of deterministic or stochastic dynamics has been shown to imply relations between fluctuation and dissipation in systems far from equilibrium, taking the form of a number of intriguing equalities, the fluctuation theorem [1, 2], the Jarzynski equality [3] and the Crooks relation [4]. In this letter, we want to stress the relation between these results and discuss their relevance by a microscopically exact study of a Joule experiment.Our theoretical starting point will be the derivation of a microcanonical version of the Crooks relation. This FIG. 1: Work distributions for a triangular object moving to the +x (upper panel) and −x direction (lower panel). Inset: detail of the multiple peak structure for τ = 5.result has the advantage that we can consider from the onset an isolated system, thereby dispensing with the need for considering a heat bath. In the limit of an infinitely large system, we recover the three above mentioned equalities. The validity and experimental observability of these relations and their interconnection can be discussed from the exact result for distribution of work when moving a convex object through an ideal gas. Consider an isolated system at time t = 0 in microcanonical equilibrium at energy E. Its Hamiltonian depends on a control parameter, which is varied during the time interval [0, t] following a specified protocol.