## Experimental Stochastic Thermodynamics

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Members of our group working in this topic:, Ignacio Martinez, Luis Dinis, Juan Manuel Rodríguez Parrondo. In collaboration with ** Édgar Roldán (MPIPKS), ** Raúl A. Rica (MAIN group, UGR) and the late Dmitri Petrov, who led the Optical Tweezers group in ICFO.

**The recent technological advances in micromanipulation and force-sensing techniques have brought access to the dynamics and energy changes that affect mesoscopic physical systems described by few degrees of freedom. For systems of microscopic and nanoscopic scale, the thermal fluctuations of the surrounding environment become relevant. Hence the dynamics of such small systems and the energy exchanges with the environment are stochastic. Motivated by the experimental access to the dynamics of Brownian particles, the emerging field of stochastic thermodynamics has been developed as a robust framework that searches for universal laws that govern the thermodynamics of systems strongly affected by thermal fluctuations. Stochastic thermodynamics has successfully extended classical thermodynamic notions like work, heat or entropy to describe thermodynamic processes that occur at the mesoscale. Currently, stochastic thermodynamics is playing a leading role in the characterization and design of efficient artificial nanomachines.The Brownian motion of microspheres in liquid has offered a model system for experimental studies of processes where thermal fluctuations are important. Very recently, our group has pioneered experimental constructions of microscopic engines using colloidal particles trapped by optical tweezers. Two major contributions of our work are the realization of one of the first single-particle Maxwell demon or Szilard engine [1] and the construction of the first Brownian Carnot engine [2]. **

**Effective heating**

The cooling or controllable attenuation of the motion of Brownian particles is an important step towards new experiments in different areas of physics. In [3] we suggest going in the opposite direction, in controlling the motion of optically trapped-spheres, namely, to increase the amplitude of their Brownian fluctuations. Applying noisy electrostatic fields to optically trapped spheres, we show that the effective kinetic temperature of a Brownian particle trapped in water can achieve 3000 K. This experimental technique allows tuning and controlling the kinetic temperature of the sphere with millisecond resolution over a wide range and along a single spatial direction, and has demonstrated extremely useful for the study of nonequilibrium thermodynamic processes at the microscopic scale [4].

**Measuring the complete Thermodynamics of a Brownian particle in water**

In [5] we developed a new technique to estimate the mean square velocity of a Brownian particle from time traces of the position of the Brownian particle sampled at low frequencies that are several orders of magnitude smaller than the momentum relaxation frequency. We apply our technique to determine the mean square velocity of single optically trapped polystyrene microspheres immersed in water.

Experimental access of the instantaneous velocity of Brownian particles is of paramount importance not only for the understanding of Brownian motion. The variations of kinetic energy that occur at the mesoscale are relevant for the detailed description of Stochastic energetics, the notion of entropy at small scales and the statement of fluctuation theorems. As we showed in later experimental works, a correct energetic description of micro and nano heat engines would only be possible taking into account the kinetic energy changes [2,4-6].

**Microadiabaticity**

The realization of adiabatic processes has remained elusive to experimentalists for decades due to the difficulty in isolating Brownian particles from their fluctuating environment. In [6] we report on the experimental realization of the first 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. Our protocols served us to implement the first microscopic engine that is able to attain the fundamental limit for the efficiency set by Carnot.

**The Brownian Carnot engine**

The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors and some artificial micro-engines operate. As described by stochastic thermodynamics, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit. In [2] we report on 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 temperatures. 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.

**Colloidal heat engines: a review**

The international recognition of the experimental achievements of our group has crystallized in a recent review on the emerging field of colloidal heat engines [7]. First, the theoretical framework of stochastic thermodynamics is revisited. Then recent implementations of the colloidal equivalents to the macroscopic Stirling, Carnot and steam engines are discussed. These small-scale motors exhibit unique features in terms of power and efficiency fluctuations that have no equivalent in the macroscopic world. In the review, a second pathway for work extraction is considered, one that consists of colloidal engines operating between active bacterial reservoirs at different temperatures, which could significantly boost the performance of passive heat engines at the mesoscale. Finally, a new generation of experiments with colloidal systems are proposed, with the focus on work extraction to generate net particle or energy currents in the mesoscale.**Selected references**

[1] Roldán, E., Martínez, I. A., Parrondo, J. M. R. & Petrov, D. Universal features in the energetics of symmetry breaking. Nature Phys. 10, 457–461 (2014)

[2] Ignacio A. Martínez, Édgar Roldán, Luis Dinis, Dmitri Petrov, J.M.R. Parrondo and Raúl A. Rica, Brownian Carnot engine. Nature Physics 12, 67–70 (2016)

[3] Ignacio A. Martínez, Edgar Roldán, Juan M. R. Parrondo, and Dmitri Petrov, Effective heating to several thousand kelvins of an optically trapped sphere in a liquid. Physical Review E 87, 032159 (2013)

[4] Pau Mestres, Ignacio A. Martínez, Antonio Ortiz-Ambriz, Raul A. Rica, and Edgar Roldán, Realization of nonequilibrium thermodynamic processes using external colored noise. Physical Review E 90 (3), 032116 (2014)

[5] Édgar Roldán, Ignacio A. Martínez, Luis Dinis, Raúl A. Rica, Measuring kinetic energy changes in the mesoscale with low acquisition rates, Applied Physics Letters 104, 234103 (2014)

[6] Ignacio A. Martínez, Édgar Roldán, Luis Dinis, Dmitri Petrov and Raúl A. Rica. Adiabatic Processes Realized with a Trapped Brownian Particle. Physical Review Letters 114, 120601 (2015)

[7] Ignacio A. Martínez, Édgar Roldán, Luis Dinis and Raúl A. Rica, Colloidal heat engines: a review. Soft Matter 2016, Advance Article