Understanding Time-reversal Symmetry of Underdamped Brownian Motion Trajectory Using Machine Learning Methods

Kiwing To^1*, Kuan-Hsi Chen²

¹Institute of Physics, Academia Sinica, Taipei, Taiwan
²Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan

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

We study the time reversal symmetry breaking of an underdamped Brownian particle (UBP) dragged by a harmonic potential trap using artificial intelligent techniques. When the potential trap is stationary, the parity-time inverted (PT) trajectories, generated by exchanging the end points of the original UBP trajectories and followed by time reversal operation, are statistically indistinguishable to the originals. However, when the harmonic potential moves with a constant speed, the PT trajectories and the original trajectories can be distinguished using a logistic regression classifier or a convolutional neural network. The performances of these classifiers are studied in terms of the speed of the potential trap and the physical time scales involved in the motion.

Keywords: under damp Brownian motion, machine learning, time reversal symmetry