The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths1. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors2 and some artificial micro-engines3–5 operate. As described by stochastic thermodynamics6,7, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit8. Here we report an experimental realization of a Carnot engine with a single optically trapped Brownian particle as the working substance. We present an exhaustive study of the energetics of the engine and analyse the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures9–11. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency—an insight that could inspire new strategies in the design of efficient nano-motors.

An ensemble of Brownian particles in a feedback controlled flashing ratchet is studied. The ratchet potential is switched on and off depending on the position of the particles, with the aim of maximizing the current. We study in detail a protocol which maximizes the instant velocity of the center of mass of the ensemble at any time. This protocol is optimal for one particle and performs better than any periodic flashing for ensembles of moderate size, but is defeated by a random or periodic switching for large ensembles.

The GTPase dynamin polymerizes into a helical coat that constricts membrane necks of endocytic pits to promote their fission. However, the dynamin mechanism is still debated because constriction is necessary but not sufficient for fission. Here, we show that fission occurs at the interface between the dynamin coat and the uncoated membrane. At this location, the considerable change in membrane curvature increases the local membrane elastic energy, reducing the energy barrier for fission. Fission kinetics depends on tension, bending rigidity, and the dynamin constriction torque. Indeed, we experimentally find that the fission rate depends on membrane tension in vitro and during endocytosis in vivo. By estimating the energy barrier from the increased elastic energy at the edge of dynamin and measuring the dynamin torque, we show that the mechanical energy spent on dynamin constriction can reduce the energy barrier for fission sufficiently to promote spontaneous fission. :

Stochastic heat engines can be built using colloidal particles trapped using optical tweezers. Here we review recent experimental realizations of microscopic heat engines. We first revisit the theoretical framework of stochastic thermodynamics that allows to describe the fluctuating behavior of the energy fluxes that occur at mesoscopic scales, and then discuss recent implementations of the colloidal equivalents to the macroscopic Stirling, Carnot and steam engines. These small-scale motors exhibit unique features in terms of power and efficiency fluctuations that have no equivalent in the macroscopic world. We also consider a second pathway for work extraction from colloidal engines operating between active bacterial reservoirs at different temperatures, which could significantly boost the performance of passive heat engines at the mesoscale. Finally, we provide some guidance on how the work extracted from colloidal heat engines can be used to generate net particle or energy currents, proposing a new generation of experiments with colloidal systems.

The ability to implement adiabatic processes in the mesoscale is of key importance in the study of artificial or biological micro-and nanoengines. Microadiabatic processes have been elusive to experimental implementation due to the difficulty in isolating Brownian particles from their fluctuating environment. Here we report on the experimental realization of a microscopic quasistatic adiabatic process employing a trapped Brownian particle. We circumvent the complete isolation of the Brownian particle by designing a protocol where both characteristic volume and temperature of the system are changed in such a way that the entropy of the system is conserved along the process. We compare the protocols that follow from either the overdamped or underdamped descriptions, demonstrating that the latter is mandatory in order to obtain a vanishing average heat flux to the particle. We provide analytical expressions for the distributions of the fluctuating heat and entropy and verify them experimentally. Our protocols could serve to implement the first microscopic engine that is able to attain the fundamental limit for the efficiency set by Carnot. [15,17,18].Until now, the design of microscopic heat engines has been restricted to those cycles formed by isothermal processes or instantaneous temperature changes [16], where the validity of a heat fluctuation theorem has been tested [19]. Recent works have shown that exerting random forces on a microscopic particle one can accurately tune the effective kinetic temperature of the particle both under equilibrium [20][21][22] and nonequilibrium driving [23]. However, the application of such a technique to implement nonisothermal processes has not been fully exploited yet [24].Among all the nonisothermal processes, adiabatic processes are of major importance in thermodynamics since they are the building blocks of the Carnot engine [25]. Microadiabaticity, i.e., true adiabaticity (TA) at the microscopic scale, cannot be realized for single trajectories due to the unavoidable heat flows between microscopic systems and their surroundings. However, a process where no net heat transfer is obtained when averaged over many trajectories, or mean adiabatic (MA) could, in principle, be realized. For simplicity, we will refer in the following MA processes as adiabatic processes.The notion of microadiabaticity has been studied theoretically since the first models of microscopic heat engines [26]. Schmiedl and Seifert devised a Brownian heat engine with two instantaneous steps in which the positional Shannon entropy of the system is conserved [27]. Further theoretical developments have considered the case of adiabatic processes in the underdamped limit [28,29]. The first experimental studies of microscopic heat engines [16] and nonisothermal processes [19] have not realized the case of adiabatic processes in the mesoscale yet.In this Letter, we report on the realization of quasistatic adiabatic processes with an optically trapped microparticle whose kinetic temperature is controlled by means ...

Abstract. -We show how to switch on and off the ratchet potential of a collective Brownian motor, depending only on the position of the particles, in order to attain a current higher than or at least equal to that induced by any periodic flashing. Maximization of instant velocity turns out to be the optimal protocol for one particle but is nevertheless defeated by a periodic switching when a sufficiently large ensemble of particles is considered. The protocol presented in this letter, although not the optimal one, yields approximately the same current as the optimal protocol for one particle and as the optimal periodic switching for an infinite number of them.Introduction. -Brownian motors, acting as thermal fluctuation rectifiers, have been attracting considerable attention in the past ten years mainly due to their potential applications in biology, condensed matter and nanotechnology but also to their theoretical relevancy in statistical mechanics [1,2]. In most of the cases, rectification is achieved by means of an external periodic or random perturbation applied to an equilibrium system with some underlying spatial or temporal asymmetry.However, it is only recently that research has been focused on introducing control in Brownian ratchets. Tarlie and Astumian studied in [3] the effect of a controllable time modulation of the applied sawtooth potential and find the modulation that maximizes particle flow. Other ways to control particle current have been proposed that are specially useful in systems where the ratchet potential parameters are not easily tunable, as in most two dimensional ratchet setups where the Brownian particles interact with an asymmetric substrate. Examples of these devices are a rectifier of magnetic flux quanta in superconductors [4] or synthetic ion channels [5]. According to Savel'ev et al., flux in some of these ratchets can be controlled by addition of other species of particles that interact with the original ones [6]. Alternatively, the application of two mixing signals could control ratchet-like particle transport of ferrofluids or dislocations in crystalline solids, pumping of electrons in quantum dots or colloids in arrays of optical tweezers [7].

We present a modification of the so-called Parrondo's paradox where one is allowed to choose in each turn the game that a large number of individuals play. It turns out that, by choosing the game which gives the highest average earnings at each step, one ends up with systematic loses, whereas a periodic or random sequence of choices yields a steadily increase of the capital. An explanation of this behavior is given by noting that the short-range maximization of the returns is "killing the goose that laid the golden eggs". A continuous model displaying similar features is analyzed using dynamic programming techniques from control theory.c EDP Sciences

Two losing gambling games, when alternated in a periodic or random fashion, can produce a winning game. This paradox has been inspired by certain physical systems capable of rectifying fluctuations: the so-called Brownian ratchets. In this paper we review this paradox, from Brownian ratchets to the most recent studies on collective games, providing some intuitive explanations of the unexpected phenomena that we will find along the way.Comment: 25 pages, 11 figure