Once we have a long enough trajectory, a second jupyter notebook should be added to the directory double_well to solve the following tasks.
Transitions matrix of the 1D projection (coordinate $X$)
Let's start with:
[ ] Define discrete states (microstates) in the 1D space (a regular bin, for instance) for the $X$ coordinate.
[ ] Get the transitions probabilities between those states observed from the trajectory with a $\Delta t = 10 ms$ and stored them as a matrix ($P_{i->j}$ for every $i$ in columns -the sum of values in every column is equal to one-).
[ ] Diagonalize the matrix to get the stationary probability distribution of the states. Compare this eigenvector with the stationary distribution observed along the trajectory.
[ ] Define an initial probability distribution with the value 1.0 in a single microstate and 0.0 for the rest of them. Get the probability distribution when the system evolves $10 ms$, $20 ms$, $30 ms$, ... with the help of the transition matrix computed before.
Once we have a long enough trajectory, a second jupyter notebook should be added to the directory
double_wellto solve the following tasks.Transitions matrix of the 1D projection (coordinate $X$)
Let's start with: