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State Space Representation01:27

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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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    Area of Science:

    • Computational chemistry
    • Statistical mechanics
    • Molecular dynamics

    Background:

    • Non-equilibrium molecular dynamics (NEMD) simulations are increasingly used for systems with external fields.
    • Recent advances include local thermostatting for reliable non-equilibrium studies.
    • Markov state models (MSMs) are established for equilibrium systems but not for non-equilibrium ones.

    Purpose of the Study:

    • To present a method for constructing non-equilibrium Markov state models (MSMs).
    • To demonstrate the validity and usefulness of non-equilibrium MSMs for analyzing molecular dynamics.
    • To apply the method to alanine dipeptide conformation dynamics in an electric field.

    Main Methods:

    • Development of a method to build MSMs from NEMD simulations.
    • Application of the method to simulate alanine dipeptide conformational changes.
    • Utilizing local thermostatting within NEMD simulations for thermodynamic consistency.

    Main Results:

    • Successfully constructed non-equilibrium MSMs for molecular systems.
    • Demonstrated the accuracy and utility of the developed MSM approach.
    • Illustrated the conformational dynamics of alanine dipeptide under an electric field using the new MSMs.

    Conclusions:

    • The proposed method allows for statistically reliable and thermodynamically consistent construction of MSMs for NEMD simulations.
    • Non-equilibrium MSMs can accurately capture the kinetics of molecular systems driven by external fields.
    • This work extends MSM applications to a broader range of non-equilibrium phenomena.