Implementation of Machine Learning in Predicting the Direction of the Thermodynamic Time Arrow in Brownian Motion

Physics undergraduate computational project, Universidad de los Andes (2023)

The thermodynamic arrow of time determines the time direction that a microscopic process takes, which can happen in a forward or a reverse direction. Using concepts such as entropy production rate and adapting the second law of thermodynamics to hold true in a stochastic context, it has been determined that processes that violate the second law of thermodynamics are those with a reverse arrow of time. On the other hand, Machine Learning has proven to be a powerful tool that allows computers to recognize patterns and learn from guided or unguided training to make predictions. In this project, the potential of Machine Learning is tested in a statistical physics context to analyze the possibility of reproducing theoretical results with just a Machine Learning model.

To predict the direction of the thermodynamic arrow of time in a particle system in brownian motion with a time-dependent quadratic potential without using the theoretical estimation, a Machine Learning classification model based on logistic regression was implemented. The theoretical estimation of the arrow of time was successfully reproduced by the model’s predictions with a 79.5 % accuracy. Similarly, the model was able to relate the work done by the brownian particle to the direction of the arrow of time, agreeing with the literature involving reversibility in the microscopic scale. This opens the possibility of expanding the use of Machine Learning in statistical physics to find new physical patterns and to observe previous patterns in novel systems.

Grupo de Física Estadística

Departamento de Física

Edificio Ip

Carrera 1E # 18A-10

Bogotá, Colombia

Universidad de los Andes | Vigilada Mineducación
Reconocimiento como Universidad: Decreto 1297 del 30 de mayo de 1964.
Reconocimiento personería jurídica: Resolución 28 del 23 de febrero de 1949 Minjusticia.

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