Despite the simplicity of the Carnot cycle, realizing it at the microscale is complicated by the difficulty in implementing adiabatic processes. A clever solution subjects a charged particle to a noisy electrostatic force that mimics a thermal bath. 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-engines3,4,5 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 temperatures9,10,11. 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 with 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 particles or energy currents, proposing a new generation of experiments with colloidal systems.

Identifying dissipation is essential for understanding the physical mechanisms underlying nonequilibrium processes. In living systems, for example, the dissipation is directly related to the hydrolysis of fuel molecules such as adenosine triphosphate (ATP). Nevertheless, detecting broken time-reversal symmetry, which is the hallmark of dissipative processes, remains a challenge in the absence of observable directed motion, flows, or fluxes. Furthermore, quantifying the entropy production in a complex system requires detailed information about its dynamics and internal degrees of freedom. Here we introduce a novel approach to detect time irreversibility and estimate the entropy production from time-series measurements, even in the absence of observable currents. We apply our technique to two different physical systems, namely, a partially hidden network and a molecular motor. Our method does not require complete information about the system dynamics and thus provides a new tool for studying nonequilibrium phenomena.

A system in equilibrium takes a finite time to relax to a new equilibrium following a sudden change of a control parameter—impeding progress in device miniaturization. Now, a strategy succeeds in reducing this time for an open classical system. A fundamental and intrinsic property of any device or natural system is its relaxation time τrelax, which is the time it takes to return to equilibrium after the sudden change of a control parameter1. Reducing τrelax is frequently necessary, and is often obtained by a complex feedback process. To overcome the limitations of such an approach, alternative methods based on suitable driving protocols have been recently demonstrated2,3, for isolated quantum and classical systems4,5,6,7,8,9. Their extension to open systems in contact with a thermostat is a stumbling block for applications. Here, we design a protocol, named Engineered Swift Equilibration (ESE), that shortcuts time-consuming relaxations, and we apply it to a Brownian particle trapped in an optical potential whose properties can be controlled in time. We implement the process experimentally, showing that it allows the system to reach equilibrium 100 times faster than the natural equilibration rate. We also estimate the increase of the dissipated energy needed to get such a time reduction. The method paves the way for applications in micro- and nano-devices, where the reduction of operation time represents as substantial a challenge as miniaturization10.

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.