4-29 September 2017
Nordita, Stockholm
Europe/Stockholm timezone

How to detect irreversibility from time-series

6 Sep 2017, 14:00
122:026 (Nordita, Stockholm)


Nordita, Stockholm


Dhrubaditya Mitra


If you look at movies of a tracer particle advected by a turbulent flow and its time-reversed version the two movies look very similar, although the system is not in equilibrium but in non-equilibrium stationary state. Can one detect that the system is indeed irreversible from this time series? This curious question has been address by several recent publications who proposed that the irreversibility manifests itself in the following way: the tracer takes long to accelerate but decelerates quickly. This has been quantified by looking at the third moment of two random variables, the power and the increment of energy over a time-scale $\tau$, defined by $W(\tau) = E(t+\tau) - E(t) $. The PDF of both of these random variables are shown to be negatively skewed. Here we extend this result to heavy inertial particles (for example water droplets in atmosphere) who follow a dissipative dynamics. We show that for the heavy inertial particles the same measure of irreversibility works. In addition, we propose a new measure : The PDF of time over which the power keeps the same sign. The tail of such PDFs are found to be exponential hence we can define a characteristic time scale of gain and loss of energy. The characteristic time scale of gain is slow compared to the time scale of loss.

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