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2024 | Book

Efficient Control and Spontaneous Transitions

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About this book

This thesis addresses deep questions that cut to the physical and informational essence of central chemical quantities such as transition paths and reaction mechanisms and proposes fundamental new connections between transition-path theory, linear-response theory, nonequilibrium thermodynamics, and information theory. The author investigates 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, an alternative perspective of transition-path theory is developed that unifies it with stochastic thermodynamics to describe flows of entropy, energy, and information during the reaction. This also provides an optimization criterion for selecting collective variables. Next, protocols are designed which invert the magnetization of a 3×3 Ising model with minimal energetic cost, and it is determined that using multiple control parameters allows the system to be driven along a fast-relaxing pathway between reaction endpoints. Finally, the author compares these 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 represents a major step forward in our understanding of rare events and provides a basis for investigating the connection between efficient protocols and spontaneous transition mechanisms which can be further probed in a wider variety of systems.

Table of Contents

Frontmatter
Chapter 1. Introduction
Abstract
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 have extended 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.
Miranda Louwerse
Chapter 2. Theoretical Background
Abstract
In this chapter, some necessary theoretical background is introduced which will inform the work in the remainder of this thesis. Section 2.1 begins with a review of stochastic dynamics, followed by some background into information theory in Sect. 2.1.2 and stochastic thermodynamics in Sect. 2.1.3. The fundamentals of transition-path theory are then reviewed in Sect. 2.2 and the utility of the committor as a reaction coordinate is discussed in more detail. In Sect. 2.3, the thermodynamics of control protocols are reviewed, followed by introduction of minimum-work protocols in the linear-response regime and the generalized friction.
Miranda Louwerse
Chapter 3. Information Thermodynamics of Transition Paths
Abstract
In this chapter, an alternative perspective of transition-path theory (which describes reactive events) is developed that unites it with stochastic thermodynamics to describe flows of entropy, energy, and information during the reaction. The main result is a quantification of the irreversibility of system dynamics while a reaction occurs, with parallel definitions of an entropy production rate and mutual information flow for transition-path dynamics. These provide a thermodynamic measure of the relevance of a particular degree of freedom to the reaction, yielding an optimization criterion for selecting collective variables that describe a reaction. (Material in this chapter also appears in Louwerse and Sivak (Phys Rev Lett 128:170602, 2022).)
Miranda Louwerse
Chapter 4. Multidimensional Minimum-Work Protocols
Abstract
In this chapter, control protocols are designed that invert the magnetization of a \(3 \times 3\) Ising model with minimal energetic cost in the slow-driving limit and compared with naive protocols. Using multiple control parameters, which provide additional flexibility in manipulating the system conformation relative to a single control parameter, allows the system to be driven along a fast-relaxing pathway between reaction endpoints. An accounting of the work done by each control parameter is also presented and analyzed (Material in this chapter also appears in Ref. Louwerse and Sivak, J. Chem. Phys. 156:194108, 2022).
Miranda Louwerse
Chapter 5. Connections Between Minimum-Work Protocols and Transition Paths
Abstract
In this chapter, a direct comparison between the designed minimum-work protocols from Chap. 4 and the spontaneous transition mechanism for magnetization inversion in a 3\(\times \)3 Ising model is presented. Designed protocols are found to capture general features of the spontaneous mechanism and energetics given the constraints on the control parameters. Based on these results, the conditions under which a strong correspondence between efficient control protocols and spontaneous transition mechanisms could be found are discussed (Material in this chapter also appears in Ref. Louwerse, Thesis code for 2D Ising model, 2022. https://​github.​com/​mdlouwerse/​MDL_​thesis_​code).
Miranda Louwerse
Chapter 6. Conclusions
Abstract
This chapter summarizes the work in this thesis and provides suggestions for future investigation of the connection between efficient protocols and spontaneous transition mechanism, outlining general directions of investigation and particular model systems.
Miranda Louwerse
Backmatter
Metadata
Title
Efficient Control and Spontaneous Transitions
Author
Miranda Louwerse
Copyright Year
2024
Electronic ISBN
978-3-031-40534-1
Print ISBN
978-3-031-40533-4
DOI
https://doi.org/10.1007/978-3-031-40534-1

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