language:en license:odbl size_categories:n<1K format:imagefolder modality:image library:datasets library:mlcroissant region:us molecular simulation brownian motion crook's fluctuation theorem
---
language: 
- en
pretty_name: Brownian Time Series Dataset
tags:
- molecular simulation
- brownian motion
- crook's fluctuation theorem
license: odbl
size_categories:
- "20000"
---

# Brownian particle trajectories dataset 

> Link to github dataset can be found [here](https://github.com/shaunak-badani/DatasetProject)

### Executive summary
    The dataset describes a set of trajectories for a brownian particle in a harmonic potential whose center also moves with time.The inspiration for this dataset comes from the paper ["Machine learning the thermodynamic arrow of time"](https://www.nature.com/articles/s41567-020-1018-2).

    The problem we're trying to solve is determining the arrow of time from a given time-series data of the particle in motion. Given a trajectory, can I determine if it is a forward trajectory (state A to state B), or if it is a backward trajectory (state B to state A)?

![Image](./images/Visual_representation.png)

    This dataset, once generated, could be used for a variety of different analyses, such as understanding the Crook's Fluctuation theorem. The methods to generate the dataset, along with the dataset, can give the necessary tools for someone interested to work on this problem with little to no domain knowledge of molecular dynamics and statistical mechanics.


### Description of data

    There are `1002` columns in this dataset.
    The first 1000 columns denote the position of the particle at that timestep. 
    The next two columns are `w`, the work done in moving the particle from the start position to the end position, and `isForward`, denoting if the trajectory is a forward trajectory or a backward trajectory.

| Column Name     | Description           | 
| ------------- |:-------------:| 
| x_i    | Denotes the position of the particle at timestep `i`. |
| w      | Work done in moving the particle from the start position to the end position.      |
| isForward | Denotes if the trajectory is a forward trajectory or a backward trajectory.     | 

### Exploratory data analysis

Exploratory data analysis has been conducted and the analysis can be found on `Dataset Analysis.ipynb`.

### Ethics statement

This synthetic dataset has been curated while adhering to ethical principles, while trying to mimic the motion of a brownian particle in the real world as closely as possible. The dataset can be regenerated with the scripts provided, to ensure that simulation techniques have been used to generate the dataset instead of cherry-picking random values. However, if the dataset is regenerated, while some of the values may change, due to ergodicity, the work distributions would still be similar to the images displayed in the documentation. All attempts have been made to avoid biases while curating the dataset, and has been curated with the intent to promote research and development practices.