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30/08/2018

QLS researcher Edgar Roldan and colleagues have published a paper in the 28 August edition of *Physical Review Letters* (DOI:https://doi.org/10.1103/PhysRevLett.121.090601). The paper is titled "Arcsine Laws in Stochastic Thermodynamics".

The distribution of the fraction of time that a thermodynamic current elapses above its average value is universal. The distribution of this type of "random time" is the same for the fluctuating electronic current in quantum dots (a), the number of ATPs hydrolyzed by small molecular motors (b) and the particle current in colloidal systems (c); it is given by Levy's arcsine law for Brownian motion (d). Image credit: Physical Review Letters |

According to Roldan, "We show that the fraction of time that any tihermodynamic current spends above its average value follows Levy's arcsine law: currents with a long "winning" or "losing" streak are the most likely ones."

The abstract for the paper states:

We show that the fraction of time that a thermodynamic current spends above its average value follows the arcsine law, a prominent result obtained by Lévy for Brownian motion. Stochastic currents with long streaks above or below their average are much more likely than those that spend similar fractions of time above and below their average. Our result is confirmed with experimental data from a Brownian Carnot engine. We also conjecture that two other random times associated with currents obey the arcsine law: the time a current reaches its maximum value and the last time a current crosses its average value. These results apply to, inter alia, molecular motors, quantum dots, and colloidal systems.

**Link to paper:** https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.090601

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