Datasets and codes of "Nonequilibrium Green-Kubo relations for hydrodynamic transport from an equilibrium-like fluctuation-response equality"

This repository contains four Python codes for ABPs simulations and four iPython codes for Kuramoto model simulations.

(Python codes for ABPs simulations)

[1] “ABPs_steady_state.py” generates a dataset containing the positions of all the particles of all times, starting from a uniform distribution across the system.

[2] “ABPs_steady_state_data_analysis.py”  analyzes the smallest-$k$ Fourier mode of data generated by [1] to deduce the transport coefficient by a Green-Kubo relation.

[3]  “ABPs_relaxation.py” generates a dataset containing the positions of all the particles of all times, starting from a uniform distribution restricted in a band centered in the system.

[4] “ABPs_relaxation_data_analysis.py” estimates the relaxation time $\tau (k)$ of $\delta {\rho }_k(t)$.

(iPython codes for Kuramoto model simulations)

[5] "Kuramoto_model_steady_state.ipynb" generates a dataset containing time series of ${\theta }_k(t){\theta }_{-k}(t)$ and ${\dot{\theta }}_k(t){\theta }_{-k}(t)$.

[6] "Kuramoto_model_steady_state_data_analysis.ipynb" analyzes the dataset generated by [5] to deduce the transport coefficient by a Green-Kubo relation.

[7] "Kuramoto_model_relaxation.ipynb" generates 100 independent datasets containing time series of $\delta {\theta }_k(t)$.

[8] "Kuramoto_model_relaxation_data_anlysis.ipynb" analyzes 100 datasets generated by [7] to estimate the relaxation time $\tau (k)$ of $|⟨\delta {\theta }_k(t)⟩|$.

(Datasets)

This repository also contains six datasets generated by the above codes:

[1] “ABPs_steady_state_data1.zip” contains 10 sets of time series of ${\rho }_k(t)$ extracted from the position data generated by the code “ABPs_steady_state.py”.

[2] “ABPs_steady_state_data2.zip” contains 10 sets of time series of $j_k(t)$ extracted from the position data generated by the code “ABPs_steady_state.py”.

[3] “ABPs_relaxation_data.zip” contains 100 sets of time series of ${\rho }_k(t)$ extracted from the position data generated by the code “ABPs_relaxation.py”.

[4] "Kuramoto_model_steady_state_data1.zip" contains 4 sets of time series of ${\theta }_k(t){\theta }_{-k}(t)$ and ${\dot{\theta }}_k(t){\theta }_{-k}(t)$ generated by the code "Kuramoto_model_steady_state.ipynb" for noise strength $(T,\sigma )=(0.01,0.01)$.

[5] "Kuramoto_model_steady_state_data2.zip" contains 4 sets of time series of ${\theta }_k(t){\theta }_{-k}(t)$ and ${\dot{\theta }}_k(t){\theta }_{-k}(t)$ generated by the code "Kuramoto_model_steady_state.ipynb" for noise strength $(T,\sigma )=(0.002,0.005)$.

[6] "Kuramoto_model_relaxation_data.zip" contains 100 sets of time series of $\delta {\theta }_k(t)$ generated by the code "Kuramoto_model_relaxation.ipynb".