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.

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 ''capacitive mixing'' (CAPMIX) technique is aimed at the extraction of energy from the salinity difference between the sea and rivers. It is based on the voltage rise that takes place at the electrodes when changing the salt concentration of the solution in which the two electrodes are dipped. In this paper, we focus on activated carbon electrodes, produced with various methods and treatments, and we measure their behaviour in CAPMIX experiments. We find that they behave as polarizable electrodes only on time scales of the order of minutes, while on longer time scales they tend to move to a specific ''spontaneous'' potential, likely due to chemical redox reactions. This analysis sheds light on the charge leakage, i.e. the loss of the stored charge due to undesired chemical reactions, which is one of the main hurdles of the CAPMIX technique when performed with activated carbon electrodes. We show that the leakage finds its origin in the tendency of the electrode to move to its spontaneous potential. Our investigation allows us to completely get rid of the leakage and demonstrates the striking result that CAPMIX cycles can be performed without an external power supply.

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 ...

An enormous dissipation of the order of 2 kJ/L takes place during the natural mixing process of fresh river water entering the salty sea. "Capacitive mixing" is a promising technique to efficiently harvest this energy in an environmentally clean and sustainable fashion. This method has its roots in the ability to store a very large amount of electric charge inside supercapacitor or battery electrodes dipped in a saline solution. Three different schemes have been studied so far, namely, Capacitive Double Layer Expansion (CDLE), Capacitive Donnan Potential (CDP) and Mixing Entropy Battery (MEB), respectively based on the variation upon salinity change of the electric double layer capacity, on the Donnan membrane potential, and on the electrochemical energy of intercalated ions.

Electrochemical cells containing two electrodes dipped in an ionic solution are widely used as charge accumulators, either with polarizable (supercapacitor) or nonpolarizable (battery) electrodes. Recent applications include desalination ("capacitive deionization") and energy extraction from salinity differences ("capacitive mixing"). In this Letter, we analyze a general relation between the variation of the electric potential as a function of the concentration and the salt adsorption. This relation comes from the evaluation of the electrical and mechanical energy exchange along a reversible cycle, which involves salt adsorption and release by the electrodes. The obtained relation thus describes a connection between capacitive deionization and capacitive mixing. We check this relation with experimental data already reported in the literature, and moreover by some classical physical models for electrodes, including polarizable and nonpolarizable electrodes. The generality of the relation makes it very useful in the study of the properties of the electric double layer.

Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work contributes to showing the use of levitated nanoparticles as a model system for stochastic bistable dynamics, with applications to a wide variety of fields.

A model of the electro-diffusion of ions in porous electrodes is applied to analyze the dynamics of capacitive-mixing extraction of energy from salinity gradients with carbon porous electrodes. The complex time-evolution of the cell voltage observed in experiments is satisfactorily described. The asymmetry on the duration of the solution-change steps performed in open circuit is found to be due to the nonlinear voltage–concentration relationship of the electric double layers and to a current that redistributes the counterions along the depth of the electrode leading to nonuniform charge and salt adsorption. The validated model is an essential tool for the design and optimization of renewable energy extraction by this technique.