The paper "Markov models of molecular kinetics: Generation and validation" by Jan-Hendrik Prinz et al. discusses the use of Markov state models (MSMs) to approximate the long-time statistical dynamics of molecules. MSMs are advantageous over traditional molecular dynamics (MD) simulations because they can mitigate the sampling problem by extracting long-time kinetic information from short trajectories and can straightforwardly calculate expectation values and statistical uncertainties of various molecular observables. The authors summarize the current state of the art in MSM generation and validation, providing new results on the approximation error of MSMs and strategies for improving their accuracy. Key points include: 1. **Approximation Error**: The authors provide an upper bound for the approximation error when modeling molecular dynamics with an MSM, showing that this error can be made arbitrarily small with minimal effort. 2. **State Space Discretization**: Contrary to previous practices, the best MSM is not obtained by the most metastable discretization. Introducing non-metastable states near transition states can improve the accuracy of the MSM. 3. **Individual Process Resolution**: It is not necessary to resolve all slow processes by state space partitioning; individual dynamical processes of interest can be described separately. 4. **Efficient Estimation**: A new estimator for reversible transition matrices is presented, which is more efficient than previous methods. 5. ** Validation**: A robust test to validate that a MSM reproduces the kinetics of molecular dynamics data is discussed. The paper also reviews the continuous dynamics of a molecular system in thermal equilibrium, introduces the transfer operator approach, and discusses the discretization of state space and the resulting discretization error. The authors emphasize the importance of choosing appropriate discretization methods to minimize the approximation error and ensure the accuracy of MSMs in describing molecular kinetics.The paper "Markov models of molecular kinetics: Generation and validation" by Jan-Hendrik Prinz et al. discusses the use of Markov state models (MSMs) to approximate the long-time statistical dynamics of molecules. MSMs are advantageous over traditional molecular dynamics (MD) simulations because they can mitigate the sampling problem by extracting long-time kinetic information from short trajectories and can straightforwardly calculate expectation values and statistical uncertainties of various molecular observables. The authors summarize the current state of the art in MSM generation and validation, providing new results on the approximation error of MSMs and strategies for improving their accuracy. Key points include: 1. **Approximation Error**: The authors provide an upper bound for the approximation error when modeling molecular dynamics with an MSM, showing that this error can be made arbitrarily small with minimal effort. 2. **State Space Discretization**: Contrary to previous practices, the best MSM is not obtained by the most metastable discretization. Introducing non-metastable states near transition states can improve the accuracy of the MSM. 3. **Individual Process Resolution**: It is not necessary to resolve all slow processes by state space partitioning; individual dynamical processes of interest can be described separately. 4. **Efficient Estimation**: A new estimator for reversible transition matrices is presented, which is more efficient than previous methods. 5. ** Validation**: A robust test to validate that a MSM reproduces the kinetics of molecular dynamics data is discussed. The paper also reviews the continuous dynamics of a molecular system in thermal equilibrium, introduces the transfer operator approach, and discusses the discretization of state space and the resulting discretization error. The authors emphasize the importance of choosing appropriate discretization methods to minimize the approximation error and ensure the accuracy of MSMs in describing molecular kinetics.