Dissipation bounds the amplification of transition rates far from equilibrium

Variational Path Sampling of Rare Dynamical Events

This article reviews the concepts and methods of variational path sampling. These methods allow computational studies of rare events in systems driven arbitrarily far from equilibrium. Based upon a statistical mechanics of trajectory space and leveraging the theory of large deviations, they provide a perspective from which dynamical phenomena can be studied with the same types of ensemble reweighting ideas that have been used for static equilibrium properties. Applications to chemical, material, and biophysical systems are highlighted.

Stochastic thermodynamic bounds on logical circuit operation

Using a thermodynamically consistent, mesoscopic model for modern complementary metal-oxide-semiconductor transistors, we study an array of logical circuits and explore how their function is constrained by recent thermodynamic uncertainty relations when operating near thermal energies. For a single NOT gate, we find operating direction-dependent dynamics and a trade-off between dissipated heat and operation time certainty. For a memory storage device, we find an exponential relationship between the memory retention time and energy required to sustain that memory state. For a clock, we find that the certainty in the cycle time is maximized at biasing voltages near thermal energy, as is the trade-off between this certainty and the heat dissipated per cycle. We identify a control mechanism that can increase the cycle time certainty without an offsetting increase in heat dissipation by working at a resonance condition for the clock. These results provide a framework for assessing the thermodynamic costs of realistic computing devices, allowing for circuits to be designed and controlled for thermodynamically optimal operation.

Splitting probabilities as optimal controllers of rare reactive events

The committor constitutes the primary quantity of interest within chemical kinetics as it is understood to encode the ideal reaction coordinate for a rare reactive event. We show the generative utility of the committor in that it can be used explicitly to produce a reactive trajectory ensemble that exhibits numerically exact statistics as that of the original transition path ensemble. This is done by relating a time-dependent analog of the committor that solves a generalized bridge problem to the splitting probability that solves a boundary value problem under a bistable assumption. By invoking stochastic optimal control and spectral theory, we derive a general form for the optimal controller of a bridge process that connects two metastable states expressed in terms of the splitting probability. This formalism offers an alternative perspective into the role of the committor and its gradients in that they encode force fields that guarantee reactivity, generating trajectories that are statistically identical to the way that a system would react autonomously.

Variational time reversal for free-energy estimation in nonequilibrium steady states

Studying the structure of systems in nonequilibrium steady states necessitates tools that quantify population shifts and associated deformations of equilibrium free-energy landscapes under persistent currents. Within the framework of stochastic thermodynamics, we establish a variant of the Kawasaki-Crooks equality that relates nonequilibrium free-energy corrections in overdamped Langevin systems to heat dissipation statistics along time-reversed relaxation trajectories computable with molecular simulation. Using stochastic control theory, we arrive at a general variational approach to evaluate the Kawasaki-Crooks equality and use it to estimate distribution functions of order parameters in specific models of driven and active matter, attaining substantial improvement in accuracy over simple perturbative methods.

Role of interactions in nonequilibrium transformations

For arbitrary nonequilibrium transformations in complex systems, we show that the distance between the current state and a target state can be decomposed into two terms: one corresponding to an independent estimate of the distance, and another corresponding to interactions, quantified using the relative mutual information between the variables. This decomposition is a special case of a more general decomposition involving successive orders of correlation or interactions among the degrees of freedom of the system. To illustrate its practical significance, we study the thermal relaxation of two interacting, optically trapped colloidal particles, where increasing pairwise interaction strength is shown to prolong the longevity of the time-dependent nonequilibrium state. Additionally, we study a system with both pairwise and triplet interactions, where our approach identifies their distinct contributions to the transformation. In more general setups where it is possible to control the strength of different orders of interactions, our findings provide a way to disentangle their effects and identify interactions that facilitate the transformation.

Nonequilibrium design strategies for functional colloidal assemblies

We use a nonequilibrium variational principle to optimize the steady-state, shear-induced interconversion of self-assembled nanoclusters of DNA-coated colloids. Employing this principle within a stochastic optimization algorithm allows us to identify design strategies for functional materials. We find that far-from-equilibrium shear flow can significantly enhance the flux between specific colloidal states by decoupling trade-offs between stability and reactivity required by systems in equilibrium. For isolated nanoclusters, we find nonequilibrium strategies for amplifying transition rates by coupling a given reaction coordinate to the background shear flow. We also find that shear flow can be made to selectively break detailed balance and maximize probability currents by coupling orientational degrees of freedom to conformational transitions. For a microphase consisting of many nanoclusters, we study the flux of colloids hopping between clusters. We find that a shear flow can amplify the flux without a proportional compromise on the microphase structure. This approach provides a general means of uncovering design principles for nanoscale, autonomous, functional materials driven far from equilibrium.

Inferring equilibrium transition rates from nonequilibrium protocols

We develop a theory for inferring equilibrium transition rates from trajectories driven by a time-dependent force using results from stochastic thermodynamics. Applying the Kawasaki relation to approximate the nonequilibrium distribution function in terms of the equilibrium distribution function and the excess dissipation, we formulate a nonequilibrium transition state theory to estimate the rate enhancement over the equilibrium rate due to the nonequilibrium protocol. We demonstrate the utility of our theory in examples of pulling of harmonically trapped particles in one and two dimensions, as well as a semiflexible polymer with a reactive linker in three dimensions. We expect our purely thermodynamic approach will find use in both molecular simulation and force spectroscopy experiments.

Kinetic reconstruction of free energies as a function of multiple order parameters

A vast array of phenomena, ranging from chemical reactions to phase transformations, are analyzed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used, especially in the presence of large free energy barriers, to estimate free energies using biasing protocols and sampling of transition paths. Kinetic reconstructions of free energy barriers of intermediate height have been performed, with respect to a single order parameter, employing the steady state properties of unconstrained simulation trajectories when barrier crossing is achievable with reasonable computational effort. Considering such cases, we describe a method to estimate free energy surfaces with respect to multiple order parameters from a steady state ensemble of trajectories. The approach applies to cases where the transition rates between pairs of order parameter values considered is not affected by the presence of an absorbing boundary, whereas the macroscopic fluxes and sampling probabilities are. We demonstrate the applicability of our prescription on different test cases of random walkers executing Brownian motion in order parameter space with an underlying (free) energy landscape and discuss strategies to improve numerical estimates of the fluxes and sampling. We next use this approach to reconstruct the free energy surface for supercooled liquid silicon with respect to the degree of crystallinity and density, from unconstrained molecular dynamics simulations, and obtain results quantitatively consistent with earlier results from umbrella sampling.

Direct Evaluation of Rare Events in Active Matter from Variational Path Sampling

Active matter represents a broad class of systems that evolve far from equilibrium due to the local injection of energy. Like their passive analogs, transformations between distinct metastable states in active matter proceed through rare fluctuations; however, their detailed balance violating dynamics renders these events difficult to study. Here, we present a simulation method for evaluating the rate and mechanism of rare events in generic nonequilibrium systems and apply it to study the conformational changes of a passive solute in an active fluid. The method employs a variational optimization of a control force that renders the rare event a typical one, supplying an exact estimate of its rate as a ratio of path partition functions. Using this method we find that increasing activity in the active bath can enhance the rate of conformational switching of the passive solute in a manner consistent with recent bounds from stochastic thermodynamics.

Reinforcement learning of rare diffusive dynamics

We present a method to probe rare molecular dynamics trajectories directly using reinforcement learning. We consider trajectories that are conditioned to transition between regions of configuration space in finite time, such as those relevant in the study of reactive events, and trajectories exhibiting rare fluctuations of time-integrated quantities in the long time limit, such as those relevant in the calculation of large deviation functions. In both cases, reinforcement learning techniques are used to optimize an added force that minimizes the Kullback-Leibler divergence between the conditioned trajectory ensemble and a driven one. Under the optimized added force, the system evolves the rare fluctuation as a typical one, affording a variational estimate of its likelihood in the original trajectory ensemble. Low variance gradients employing value functions are proposed to increase the convergence of the optimal force. The method we develop employing these gradients leads to efficient and accurate estimates of both the optimal force and the likelihood of the rare event for a variety of model systems.

Molecular Properties and Chemical Transformations Near Interfaces

The properties of bulk water and aqueous solutions are known to change in the vicinity of an interface and/or in a confined environment, including the thermodynamics of ion selectivity at interfaces, transition states and pathways of chemical reactions, and nucleation events and phase growth. Here we describe joint progress in identifying unifying concepts about how air, liquid, and solid interfaces can alter molecular properties and chemical reactivity compared to bulk water and multicomponent solutions. We also discuss progress made in interfacial chemistry through advancements in new theory, molecular simulation, and experiments.

Dissipation bounds the amplification of transition rates far from equilibrium

Complex systems can convert energy imparted by nonequilibrium forces to regulate how quickly they transition between long-lived states. While such behavior is ubiquitous in natural and synthetic systems, currently there is no general framework to relate the enhancement of a transition rate to the energy dissipated or to bound the enhancement achievable for a given energy expenditure. We employ recent advances in stochastic thermodynamics to build such a framework, which can be used to gain mechanistic insight into transitions far from equilibrium. We show that under general conditions, there is a basic speed limit relating the typical excess heat dissipated throughout a transition and the rate amplification achievable. We illustrate this tradeoff in canonical examples of diffusive barrier crossings in systems driven with autonomous and deterministic external forcing protocols. In both cases, we find that our speed limit tightly constrains the rate enhancement.

Phase Diagram of Active Brownian Spheres: Crystallization and the Metastability of Motility-Induced Phase Separation

Motility-induced phase separation (MIPS), the phenomenon in which purely repulsive active particles undergo a liquid-gas phase separation, is among the simplest and most widely studied examples of a nonequilibrium phase transition. Here, we show that states of MIPS coexistence are in fact only metastable for three-dimensional active Brownian particles over a very broad range of conditions, decaying at long times through an ordering transition we call active crystallization. At an activity just above the MIPS critical point, the liquid-gas binodal is superseded by the crystal-fluid coexistence curve, with solid, liquid, and gas all coexisting at the triple point where the two curves intersect. Nucleating an active crystal from a disordered fluid, however, requires a rare fluctuation that exhibits the nearly close-packed density of the solid phase. The corresponding barrier to crystallization is surmountable on a feasible timescale only at high activity, and only at fluid densities near maximal packing. The glassiness expected for such dense liquids at equilibrium is strongly mitigated by active forces, so that the lifetime of liquid-gas coexistence declines steadily with increasing activity, manifesting in simulations as a facile spontaneous crystallization at extremely high activity.