title: Brownian Carnot engine.
abstract: 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.
authors.affiliation: ICFO-Institut de Ciències Fotòniques, Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.|Laboratoire de Physique, École Normale Supérieure, CNRS UMR5672 46 Allée d'Italie, 69364 Lyon, France.
authors.forename: I A
authors.initials: IA
authors.lastname: Martínez
authors.affiliation: ICFO-Institut de Ciències Fotòniques, Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.|Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany.|GISC-Grupo Interdisciplinar de Sistemas Complejos, 28040 Madrid, Spain.
authors.forename: É
authors.initials: É
authors.lastname: Roldán
authors.affiliation: GISC-Grupo Interdisciplinar de Sistemas Complejos, 28040 Madrid, Spain.|Departamento de Fisica Atómica, Molecular y Nuclear, Universidad Complutense Madrid, 28040 Madrid, Spain.
authors.forename: L
authors.initials: L
authors.lastname: Dinis
authors.affiliation: ICFO-Institut de Ciències Fotòniques, Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.
authors.forename: D
authors.initials: D
authors.lastname: Petrov
authors.affiliation: GISC-Grupo Interdisciplinar de Sistemas Complejos, 28040 Madrid, Spain.|Departamento de Fisica Atómica, Molecular y Nuclear, Universidad Complutense Madrid, 28040 Madrid, Spain.
authors.forename: J M R
authors.initials: JMR
authors.lastname: Parrondo
authors.affiliation: ICFO-Institut de Ciències Fotòniques, Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.
authors.forename: R A
authors.initials: RA
authors.lastname: Rica