Time reversal asymmetry of Brownian trajectories in non-equilibrium steady state granular gas using machine learning method

Kiwing To^1*, Chi-Ho Chou¹

¹Institute of Physics, Academia Sinica, Taipei, Taiwan

* Presenter:Kiwing To, email:ericto@gate.sinica.edu.tw

The trajectories of a colloidal particle (CP) in a fluid at thermodynamic equilibrium (TE) are time reversal symmetric such that the probability of a particular trajectory (AT) equals the probability of the party-time inverted trajectory (PT) generated by exchanging the end points of the original trajectory and followed by time reversal operation. This is true even when the CP is trapped by a stationary potential well. However, when the potential well moves and drags the CP along, the trajectories of the CP will not be time reversal symmetric because the process is non-equilibrium. The second law of thermodynamics (fluctuation theorem) provides a quantitative measure of the time reversal asymmetry (TRA) which can be calculated from the accuracy of a trained convolutional neural network (CNN). While the above had been tested for a CP in a fluid which is at TE, it has not been tested if the fluid is out of equilibrium. Will the fluctuation theorem hold if the fluid is at non-equilibrium steady state (NESS)? Hence, we collected trajectories from molecular dynamic simulations (using LAMMPS) of a CP in a granular gas at NESS. Half of the trajectories and their corresponding PTs were used to train a CNN as a classifier to distinguish the ATs from the PTs. Then the rest were used to evaluate the accuracy of the trained CNN. We find that the fluctuation theorem is indeed applicable to CP in a fluid which is at NESS.

Keywords: non-equilibrium steady state, granular fluid, fluctuation theorem, machine learning