Arcsine Laws in Stochastic Systems

Repo for a rotation project in the Biological Complexity Unit. Arcsine laws for T1, T2, and T3 as defined in Arcsine Laws in Stochastic Thermodynamics for a model of ATP hydrolysis by myosin, a colloidal particle, and a minimal biochemical engine from A Minimal Model for Carnot Efficiency at Maximum Power.

Repo directory:

• engine_sim.py - Simulation of stochastic work and heat for the biochemical engine via Gillespie algorithm

• atp_hydrolysis_sim.py - Simulation of stochastic work and heat for myosin model via Gillespie algorithm

• colloidal_sim.py - Simulation of the position trajectory for the colloidal particle via numerical evolution of Langevin equation

• trajectory_avg.py - Compute average trajectory from simulated trajectories

• get_prob_distr.py - Compute T1, T2, and T3 values for trajectories

• time_over.py - Compute T1 for a trajectory

• last_time.py - Compute T2 for a trajectory

• max_time.py - Compute T3 for a trajectory

• t_distr.py - Script to run the numerical scheme from start to finish. Returns the T distribution for a given model.

• ksstat.py - Compute the Kolmogorov-Smirnov statistic for a given T distribution

• convert_trajectory.py - Discretise trajectories in time obtained from Gillespie algorithm. This is only used for illustrative purposes.

• run_data.py - Script to run the scheme for various parameter values for each model. Computed on a cluster.

• run_data_engine_eh.py - Same as above, but for various values of the high energy state in the biochemical engine model.

• run_data_engine_s.py - Same as above, for various values of the entropy between the two states in the engine model.

• ksplots.ipynb - Jupyter notebook to generate the KS statistic and CDF comparison plots

• plots.ipynb - Jupyter notebook to generate example plots for the definitions of T1, T2, and T3

Each run of t_distr.py saves the following .pkl files:

• filename_trajs_time - dictionary of transition times obtained from Gillespie algorithm
• filename_trajs_heat - dictionary of stochastic heat trajectories
• filename_trajs_work - dictionary of stochastic work trajectories
• filename_trajs_post - dictionary of position trajectories
• filename_avgtrajs_time - average trajectory times
• filename_avgtrajs_heat - average stochastic heat trajectory
• filename_avgtrajs_work - average stochastic work trajectory
• filename_avgtrajs_post - average position trajectory
• filename_fitparams - slope and intercept values from line of best fit
• filename_tvals - values for T1, T2, and T3 for each trajectory simulation, i.e. the data for a histogram of T values