Free Energy Transduction in Chemical Reaction Networks

Energy conversion is fundamental to both living and nonliving processes, relying on the coupling of free energy-releasing and free energy-consuming steps---a mechanism known as free energy transduction. Chemistry provides an ideal platform for studying this phenomenon, as chemical reaction networks (CRNs) encompass a wide range of energy conversion mechanisms across scales, from molecular motors to macroscopic systems. Understanding the mechanisms of free energy transduction in chemistry is crucial for elucidating the behavior of both biological and artificial systems. The primary aim of this thesis is to uncover some of the principles underlying chemical free energy transduction across different contexts. The first part of this work clarifies the previously unclear relationship between transduction occurring within two different types of CRNs---tightly and loosely coupled networks. We introduce the concept of `chemical gears', which identify the distinct transduction pathways---tightly coupled subnetworks---within a loosely coupled CRN. These gears enable a refined understanding of the Second law of thermodynamics and allow for the determination of the CRN’s optimal transduction efficiency solely based on its network topology and operating conditions. Moreover, we demonstrate through a simple example that CRNs can self-regulate their gear system by adjusting reaction kinetics, thereby maintaining optimal efficiency across varying conditions. Applying this framework to artificial molecular motors reveals that their gearing mechanisms are suboptimally regulated. The second part extends the traditional framework of free energy transduction to encompass multi-resource transduction in open CRNs under steady state conditions. We develop a systematic approach to defining efficiency, inspired by methods used for thermal engines operating between multiple heat baths. We anchor the definition of efficiency in exergy---the maximum work extractable from a nonequilibrium system embedded in a reference environment---and highlight its inherently relative nature. Our definition also offers flexibility, as it can account for downstream losses not considered by the CRN. Additionally, we generalize the concept of chemical gears to multi-resource transduction, demonstrating their analytical power even in this more complex setting. Applying this framework to central metabolic pathways provides new insights into their operation. In the third part, we study a transduction mechanism that is inherently stochastic in nature. Specifically, we examine information-mediated transduction in a chemical Maxwell demon that harnesses thermal fluctuations of chemical reactions. We characterize its transduction operation, scaling behavior in the macroscopic limit, and compare it with an analogous previously studied electronic demon. Additionally, we analyze the demon’s information thermodynamics, quantifying the partial transduction efficiencies associated with the measurement and feedback processes. The fourth part of this thesis explores transduction in a nonautonomous setting, focusing on a model of an artificial molecular motor subject to time-dependent driving. We examine its relationship with the no-pumping theorem, which defines the conditions required for external driving to induce directed motion. In the slow-driving limit, we fully characterize the motor’s dynamics, while in more general regimes, we analyze its performance for a specific class of driving protocols, identifying optimal trade-offs between transduction efficiency and output power. The final part of this thesis, which is not strictly confined to chemical reaction networks, adopts an autonomous perspective on nonautonomous systems. Specifically, it investigates transduction in a class of composite stochastic systems where the degree of freedom generating the protocol is incorporated within the system, making it self-contained. For this class of systems, we introduce a systematic classification of protocols, providing a rigorous definition of concepts such as energy and information ratchets. By extending the no-pumping theorem to stochastic protocols, we determine the conditions under which transduction is possible and whether it is mediated by energy or information. We also show how the gear concept developed earlier for CRNs emerges in this framework. These findings offer a deeper insight into the thermodynamics of free energy transduction in chemistry and stochastic systems, with potential applications ranging from the design of artificial molecular motors to understanding the optimization of free energy conversion in biological systems.