Efficient control and spontaneous transitions

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. Developments in recent decades in transition-path theory, transition-path sampling, and single-molecule experimental techniques have transformed our ability to observe biomolecular reactions in microscopic detail and extract general features of the mechanism. Nearly simultaneously, rapid developments in the field of stochastic thermodynamics extend familiar notions of work, heat, and entropy to nonequilibrium contexts. One focus of these efforts is the design of protocols that dynamically manipulate the system's conformation with minimal energetic cost. In this thesis, I investigate slow, energetically efficient driving protocols that drive a system between conformations corresponding to endpoints of a reaction, aiming to find connections between principles of efficient driving and the spontaneous transition mechanism in the absence of driving. First, I develop an alternative perspective of transition-path theory (which describes reactive events) that unites it with stochastic thermodynamics to describe flows of entropy, energy, and information during the reaction. This also provides a thermodynamic measure of the relevance of a particular degree of freedom to the reaction, providing an optimization criterion for selecting collective variables. Next, I design protocols that invert the magnetization of a 3x3 Ising model with minimal energetic cost, 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 in the same Ising model, 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 protocols and spontaneous transition mechanism which can be further probed in a wider variety of systems.