The Statistical Dynamics of Nonequilibrium Control

Living systems, even at the scale of single molecules, are constantly adapting to changing environmental conditions. The physical response of a nanoscale system to external gradients or changing thermodynamic conditions can be chaotic, nonlinear, and hence difficult to control or predict. Nevertheless, biology has evolved systems that reliably carry out the cell’s vital functions efficiently enough to ensure survival. Moreover, the development of new experimental techniques to monitor and manipulate single biological molecules has provided a natural testbed for theoretical investigations of nonequilibrium dynamics. This work focuses on developing paradigms for both understanding the principles of nonequilibrium dynamics and also for controlling such systems in the presence of thermal fluctuations. Throughout this work, I rely on a perspective based on two central ideas in nonequilibrium statistical mechanics: large deviation theory, which provides a formalism akin to thermodynamics for nonequilibrium systems, and the fluctuation theorems which identify time symmetry breaking with entropy production. I use the tools of large deviation theory to explore concepts like efficiency and optimal coarse-graining in microscopic dynamical systems. The results point to the extreme importance of rare events in nonequilibrium dynamics. In the context of rare dynamical events, I outline a formal approach to predict efficient control protocols for nonequilibrium systems and develop computational tools to solve the resulting high dimensional optimization problems. The final chapters of this work focus on applications to self-assembly dynamics. I show that the yield of desired structures can be enhanced by driving a system away from equilibrium, using analysis inspired by the theory of the hydrophobic effect. Finally, I demonstrate that nanoscale, protein shells can be modeled and controlled to robustly produce monodisperse, nonequilibrium structures strikingly similar to the microcompartments observed in a variety of bacteria

Efficiency and Large Deviations in Time-Asymmetric Stochastic Heat Engines

In a stochastic heat engine driven by a cyclic non-equilibrium protocol, fluctuations in work and heat give rise to a fluctuating efficiency. Using computer simulations and tools from large deviation theory, we have examined these fluctuations in detail for a model two-state engine. We find in general that the form of efficiency probability distributions is similar to those described by Verley et al. [2014 Nat Comm, 5 4721], in particular featuring a local minimum in the long-time limit. In contrast to the time-symmetric engine protocols studied previously, however, this minimum need not occur at the value characteristic of a reversible Carnot engine. Furthermore, while the local minimum may reside at the global minimum of a large deviation rate function, it does not generally correspond to the least likely efficiency measured over finite time. We introduce a general approximation for the finite-time efficiency distribution, $P(\eta)$, based on large deviation statistics of work and heat, that remains very accurate even when $P(\eta)$ deviates significantly from its large deviation form.Comment: 10 pages, 3 figure

Near-optimal protocols in complex nonequilibrium transformations

The development of sophisticated experimental means to control nanoscale systems has motivated efforts to design driving protocols which minimize the energy dissipated to the environment. Computational models are a crucial tool in this practical challenge. We describe a general method for sampling an ensemble of finite-time, nonequilibrium protocols biased towards a low average dissipation. We show that this scheme can be carried out very efficiently in several limiting cases. As an application, we sample the ensemble of low-dissipation protocols that invert the magnetization of a 2D Ising model and explore how the diversity of the protocols varies in response to constraints on the average dissipation. In this example, we find that there is a large set of protocols with average dissipation close to the optimal value, which we argue is a general phenomenon.Comment: 6 pages and 3 figures plus 4 pages and 5 figures of supplemental materia

Microscopic origin of tunable assembly forces in chiral active environments

The fluctuations of a nonequilibrium bath enable dynamics inaccessible to any equilibrium system. Exploiting the driven dynamics of active matter in order to do useful work has become a topic of significant experimental and theoretical interest. Due to the unique modalities controlling self-assembly, the interplay between passive solutes and the particles in an active bath has been studied as a potential driving force to guide assembly of otherwise non-interacting objects. Here, we investigate and characterize the microscopic origins of the attractive and repulsive interactions between passive solutes in an active bath. We show that, while assembly does not occur dynamically for achiral active baths, chiral active particles can produce stable and robust assembly forces. We both explain the observed oscillatory force profile for active Brownian particles and demonstrate that chiral active motion leads to fluxes consistent with an odd diffusion tensor that, when appropriately tuned, produces long-ranged assembly forces