Édgar Roldán

Universal features in the energetics of symmetry breaking

The spontaneous breaking of a system’s symmetry results in an entropy decrease. Now, an experiment involving a particle subject to a potential with a shape that changes from a single- to a double-well demonstrates that the associated entropy changed is detectable. Moreover, the experimental setup enables the realization of a Szilard engine.

Brownian Carnot engine

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.

Adiabatic processes realized with a trapped Brownian particle.

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.

Mechanisms of backtrack recovery by RNA polymerases I and II

Significance Transcription of the genetic information from DNA into RNA is the central process of gene expression, and it is performed by enzymes called RNA polymerases (Pol). Transcription is interspersed with a proofreading mechanism called backtracking, during which the polymerase moves backward on the DNA template and displaces the RNA 3′ end from its active site. Backtrack recovery can happen by diffusion of the enzyme along the DNA or cleavage of the backtracked RNA. Using single-molecule optical tweezers and stochastic theory, we quantified distinct diffusion and cleavage rates of Pol I and Pol II and described distinct backtrack recovery strategies of these essential enzymes. During DNA transcription, RNA polymerases often adopt inactive backtracked states. Recovery from backtracks can occur by 1D diffusion or cleavage of backtracked RNA, but how polymerases make this choice is unknown. Here, we use single-molecule optical tweezers experiments and stochastic theory to show that the choice of a backtrack recovery mechanism is determined by a kinetic competition between 1D diffusion and RNA cleavage. Notably, RNA polymerase I (Pol I) and Pol II recover from shallow backtracks by 1D diffusion, use RNA cleavage to recover from intermediary depths, and are unable to recover from extensive backtracks. Furthermore, Pol I and Pol II use distinct mechanisms to avoid nonrecoverable backtracking. Pol I is protected by its subunit A12.2, which decreases the rate of 1D diffusion and enables transcript cleavage up to 20 nt. In contrast, Pol II is fully protected through association with the cleavage stimulatory factor TFIIS, which enables rapid recovery from any depth by RNA cleavage. Taken together, we identify distinct backtrack recovery strategies of Pol I and Pol II, shedding light on the evolution of cellular functions of these key enzymes.

Generic Properties of Stochastic Entropy Production

We derive an Itô stochastic differential equation for entropy production in nonequilibrium Langevin processes. Introducing a random-time transformation, entropy production obeys a one-dimensional drift-diffusion equation, independent of the underlying physical model. This transformation allows us to identify generic properties of entropy production. It also leads to an exact uncertainty equality relating the Fano factor of entropy production and the Fano factor of the random time, which we also generalize to non-steady-state conditions.

Decision Making in the Arrow of Time

We show that the steady-state entropy production rate of a stochastic process is inversely proportional to the minimal time needed to decide on the direction of the arrow of time. Here we apply Walds sequential probability ratio test to optimally decide on the direction of times arrow in stationary Markov processes. Furthermore, the steady-state entropy production rate can be estimated using mean first-passage times of suitable physical variables. We derive a first-passage time fluctuation theorem which implies that the decision time distributions for correct and wrong decisions are equal. Our results are illustrated by numerical simulations of two simple examples of nonequilibrium processes.

Realization of nonequilibrium thermodynamic processes using external colored noise.

We investigate the dynamics of single microparticles immersed in water that are driven out of equilibrium in the presence of an additional external colored noise. As a case study, we trap a single polystyrene particle in water with optical tweezers and apply an external electric field with flat spectrum but a finite bandwidth of the order of kHz. The intensity of the external noise controls the amplitude of the fluctuations of the position of the particle and therefore of its effective temperature. Here we show, in two different nonequilibrium experiments, that the fluctuations of the work done on the particle obey the Crooks fluctuation theorem at the equilibrium effective temperature, given that the sampling frequency and the noise cutoff frequency are properly chosen.

Thermodynamics at the microscale: from effective heating to the Brownian Carnot engine

We review a series of experimental studies of the thermodynamics of nonequilibrium processes at the microscale. In particular, in these experiments we studied the fluctuations of the thermodynamic properties of a single optically-trapped microparticle immersed in water and in the presence of external random forces. In equilibrium, the fluctuations of the position of the particle can be described by an effective temperature that can be tuned up to thousands of Kelvins. Isothermal and non-isothermal thermodynamic processes that also involve changes in a control parameter were implemented by controlling the effective temperature of the particle and the stiffness of the optical trap. Since truly adiabatic processes are unfeasible in colloidal systems, mean adiabatic protocols where no average heat is exchanged between the particle and the environment are discussed and implemented. By concatenating isothermal and adiabatic protocols, it is shown how a single-particle Carnot engine can be constructed. Finally, we provide an in-depth study of the fluctuations of the energetics and of the efficiency of the cycle.

Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes

We study the statistics of infima, stopping times and passage probabilities of entropy production in nonequilibrium steady states, and show that they are universal. We consider two examples of stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches for the first time a given state. Our main results are: (i) the distribution of the global infimum of entropy production is exponential with mean equal to minus Boltzmanns constant; (ii) we find the exact expressions for the passage probabilities of entropy production to reach a given value; (iii) we derive a fluctuation theorem for stopping-time distributions of entropy production. These results have interesting implications for stochastic processes that can be discussed in simple colloidal systems and in active molecular processes. In particular, we show that the timing and statistics of discrete chemical transitions of molecular processes, such as, the steps of molecular motors, are governed by the statistics of entropy production. We also show that the extreme-value statistics of active molecular processes are governed by entropy production, for example, the infimum of entropy production of a motor can be related to the maximal excursion of a motor against the direction of an external force. Using this relation, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases, which follows from our universal results for entropy-production infima.

Measuring kinetic energy changes in the mesoscale with low acquisition rates

We report on the measurement of the average kinetic energy changes in isothermal and non-isothermal quasistatic processes in the mesoscale, realized with a Brownian particle trapped with optical tweezers. Our estimation of the kinetic energy change allows to access to the full energetic description of the Brownian particle. Kinetic energy estimates are obtained from measurements of the mean square velocity of the trapped bead sampled at frequencies several orders of magnitude smaller than the momentum relaxation frequency. The velocity is tuned applying a noisy electric field that modulates the amplitude of the fluctuations of the position and velocity of the Brownian particle, whose motion is equivalent to that of a particle in a higher temperature reservoir. Additionally, we show that the dependence of the variance of the time-averaged velocity on the sampling frequency can be used to quantify properties of the electrophoretic mobility of a charged colloid. Our method could be applied to detect temperature gradients in inhomogeneous media and to characterize the complete thermodynamics of biological motors and of artificial micro and nanoscopic heat engines.