Efficient Control and Spontaneous Transitions

Synopsis

Quantifying the dynamics and energetics of a system as it undergoes a transition between stable conformations is central to the study of reaction mechanisms and the derivation of reaction rates. For conformational changes in biomolecules, the space the system navigates is high dimensional, presenting challenges to the observation of reactive events in simulation or experiment and obscuring dynamical details that are relevant to the reaction mechanism. In this talk, we investigate the correspondence between transition-path theory, which describes the spontaneous reaction mechanism, and minimum-work protocols which drive the system between conformations corresponding to the endpoints of a reaction. We first review transition-path theory and provide a novel perspective on reactive dynamics that unites them with concepts from stochastic thermodynamics. This provides a thermodynamic measure of the relevance of a particular degree of freedom to the reaction, providing an optimization criterion for selecting collective variables. We then investigate minimum-work protocols for inverting magnetization in a 3x3 Ising model, determining that using multiple control parameters, which provide additional flexibility in manipulating the system conformation, allows it to be driven along a fast-relaxing pathway between reaction endpoints. Finally, I directly compare these designed protocols with the spontaneous transition mechanism for magnetization inversion, finding that designed protocols capture general features of the spontaneous mechanism and energetics given the constraints on the control parameters. This work provides a basis for investigating the connection between efficient driving and spontaneous reaction mechanisms which can be further probed in a wider variety of systems.

Full schedule at

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