### Martingale theory for housekeeping heat

R. Chetrite, S. Gupta, I. Neri and **É. Roldán**

arXiv:1810.09584 (2018)

The housekeeping heat is the energy exchanged between a system and its environment in a nonequilibrium process that results from the violation of detailed balance.

We describe fluctuations of the housekeeping heat in mesoscopic systems using the theory of martingales, a mathematical framework widely used in probability theory and finance.

We show that the exponentiated housekeeping heat (in units of kT, with k the Boltzmann constant and T the temperature) of a Markovian nonequilibrium process under arbitrary time-dependent driving is a martingale process. From this result, we derive universal equalities and inequalities for the statistics of stopping-times and suprema of the housekeeping heat.

### Arcsine Laws in Stochastic Thermodynamics

**A. C. Barato*, É. Roldán***, I. A. Martínez and S. Pigolotti

Physical Review Letters **121**, 090601 (2018)

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(* equal contribution)

We demonstrate with theory and experiment that the fraction of time a thermodynamic current elapses above its average value follows the arcsine law, a prominent result obtained by Levy for independent random variables.

Stochastic currents with long streaks above or below their average are much more likely than those that spend similar fraction of times above and below their average.

We demonstrate this result with simulations of molecular motors, quantum dots and colloidal systems, and with experimental data of a Brownian Carnot engine.

### Multiplex Decomposition of Non-Markovian Dynamics and the Hidden Layer Reconstruction Problem

L. Lacasa, I. P. Mariño, J. Miguez, V. Nicosia, **É. Roldán**, A. Lisica, S. W. Grill, and J. Gómez-Gardeñes

Physical Review X **8**, 031038 (2018)

We show that by using local information provided by a random walker navigating the aggregated network, it is possible to determine, in a robust manner, whether these dynamics can be more accurately represented by a single layer or if they are better explained by a (hidden) multiplex structure. In the latter case, we also provide Bayesian methods to estimate the most probable number of hidden layers and the model parameters, thereby fully reconstructing its architecture. We apply our method to experimental recordings from (i) the mobility dynamics of human players in an online multiplayer game and (ii) the dynamics of RNA polymerases at the single-molecule level.

### Arrow of Time in Active Fluctuations

**É. Roldán**, J. Barral, P. Martin, J.M.R. Parrondo and F. Jülicher

arXiv:1801.01574 (2018)

We introduce lower bounds for the rate of entropy production of an active stochastic process by quantifying the irreversibility of stochastic traces obtained from mesoscopic degrees of freedom. Our measures of irreversibility reveal signatures of time’s arrow and provide bounds for entropy production even in the case of active fluctuations that have no drift. We apply these irreversibility measures to experimental spontaneous hair-bundle oscillations from the ear of the bullfrog.

### Testing Optimality of Sequential Decision-Making

M. Dörpinghaus, I. Neri, **É. Roldán**, H. Meyr and F. Jülicher

arXiv:1801.01574 (2018)

We introduce a statistical method to test whether a system that performs a binary sequential hypothesis test is optimal in the sense of minimizing the average decision times while taking decisions with given reliabilities. The proposed method requires samples of the decision times, the decision outcomes, and the true hypotheses, but does not require knowledge on the statistics of the observations or the properties of the decision-making system. We illustrate these tests with numerical simulations and discuss potential applications in machine learning and biology.

### Records of entropy production in an electronic double dot

S. Singh,** É. Roldán**, I. Neri, I. M. Khaymovich, D. S. Golubev,

V. F. Maisi, J. T. Peltonen, F. Jülicher and J. P. Pekola

https://arxiv.org/abs/1712.01693 (2017)

We measure single-electron fluctuations in a nanoelectronic device, a double dot, sealed at very low temperature 50mK.

Statistics of millions of records in the double dot confirm that entropy production’s average negative record cannot be below minus the Boltzmann constant. Moreover the data reveals a new bound for the maximal heat absorption of a nanoscopic system from its environment.

### Generic properties of stochastic entropy production

S. Pigolotti, I. Neri, **É. Roldán** and F. Jülicher

Physical Review Letters **119** (14), 140604 (2017)

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Introducing a random-time transformation, entropy production obeys a one-dimensional Ito drift-diffusion equation, independent of the underlying physical model.

This transformation leads to an exact uncertainty equality between the Fano factor of entropy production and the Fano factor of the entropic time.

### Colloidal heat engines: A review

**É. Roldán**, L. Dinis, and R. A. Rica

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We review recent experimental constructions of small heat engines which are the colloidal equivalents to the macroscopic Stirling, Carnot and steam engines, whose fluctuations lead to unique phenomena that have no equivalent in the macroscopic world. We also discuss the work extraction from bacterial reservoirs.

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.

### Path-integral formalism for stochastic resetting:

Exactly solved examples and shortcuts to confinement

**É. Roldán** and S. Gupta

Physical Review E **96** (2), 022130 (2017)

[ **PDF** ]

We present a path-integral approach to derive analytical expressions for a variety of statistics of the dynamics of overdamped Brownian particles under stochastic resetting.

We find that using energy-dependent resetting processes is more effective in achieving spatial confinement of Brownian particles on a faster time scale than performing quenches of parameters of the harmonic potential.

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

I. Neri, **É. Roldán**, and F. Jülicher

Physical Review X **7** , 011019 (2017)

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### Brownian Carnot engine

I. A. Martínez*, **É. Roldán***, L. Dinis, J. M. R. Parrondo, D. Petrov and R. A. Rica

Nature Physics **12**, 67-70 (2016)

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### Mechanisms of backtrack recovery in RNA polymerases I and II

A. Lisica, C. Engel, M. Jahnel, **É. Roldán**, E. A. Galburt, P. Cramer and S. W. Grill

PNAS **113** (11), 2946-2951 (2016)

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### Stochastic resetting in backtrack recovery by RNA polymerases

**É. Roldán**, A. Lisica, D. Sánchez-Taltavull, and S. W. Grill

### Decision Making in the Arrow of time

**É. Roldán**, I. Neri, M. Dörpinghaus, H. Meyr, F. Jülicher

Physical Review Letters

**115**(25), 250602 (2015)

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### Fluctuation theorem between non-equilibrium states in an RC circuit

**É. Roldán**, S. Ciliberto, and H. Kantz

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### Adiabatic processes realized with a trapped Brownian particle

**É. Roldán**, L. Dinis, D. Petrov, and R. A. Rica

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### Realization of nonequilibrium thermodynamic processes using external colored noise

**É. Roldán**

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### Universal features in the energetics of symmetry breaking

**É. Roldán***, I. A. Martínez*, J. M. R. Parrondo, and D. Petrov

### Irreversibility and dissipation in microscopic systems

**É. Roldán** (Springer-Nature, Berlin, 2014)

Springer Theses Prize

[ **Link** ]

### Measuring kinetic energy changes in the mesoscale with low acquisition rates

**É. Roldán**, I. A. Martínez, L. Dinis, and R. A. Rica

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### Effective heating to several thousand kelvins of an optically trapped sphere in a liquid

**É. Roldán**, J. M. R. Parrondo, and D. Petrov

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### Time series irreversibility: a visibility graph approach

**É. Roldán**, J. M. R. Parrondo, and B. Luque

[ **PDF** ]

### Entropy production and Kullback-Leibler divergence between stationary trajectories of discrete systems

**É. Roldán**and J. M. R. Parrondo

[ **PDF** ]