## Dynamical properties describe the way collective behaviors cause macroscopic observables to redistribute or decay

## Evaluation of transport coefficients requires non-equilibrium condition

- NEMD imposes macroscopic non-equilibrium steady state
- EMD approach uses natural fluctuations from equilibrium

## Two formulations to connect macroscopic to microscopic

- Einstein relation describes long-time asymptotic behavior
- Green-Kubo relation connects to time correlation function

## Several approaches to evaluation of correlation functions

- direct: simple but inefficient
- Fourier transform: less simple, more efficient
- coarse graining: least simple, most efficient, approximate

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