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1. Dissipation rates from experimental uncertainty

   https://doi.org/10.1103/PhysRevResearch.7.L012078  

   Ghosal, Aishani; Green, Jason R (March 2025, Physical Review Research)

   Active matter and driven systems exhibit statistical fluctuations in density and particle positions that are an indirect indicator of dissipation across length and time scales. Here, we quantitatively relate these fluctuations to a thermodynamic speed limit that constrains the rates of heat and entropy production in nonequilibrium processes. By reparametrizing the speed limit set by the Fisher information, we show how to infer these dissipation rates from directly observable or controllable quantities. This approach can use available experimental data as input and avoid the need for analytically solvable microscopic models or full time-dependent probability distributions. The heat rate we predict agrees with experimental measurements for a pulled Brownian particle and a microtubule active gel, which validates the approach and suggests potential for the design of experiments. 

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2. Deep learning probability flows and entropy production rates in active matter

   https://doi.org/10.1073/pnas.2318106121  

   Boffi, Nicholas M; Vanden-Eijnden, Eric (June 2024, Proceedings of the National Academy of Sciences)

   Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. They involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry. Yet, their efficient computation has remained elusive, as they depend on the system’s unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework to estimate the score of this density. We show that the score, together with the microscopic equations of motion, gives access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles. To represent the score, we introduce a spatially local transformer network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of active particles undergoing motility-induced phase separation (MIPS). We show that a single network trained on a system of 4,096 particles at one packing fraction can generalize to other regions of the phase diagram, including to systems with as many as 32,768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction. 

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3. Markov State Model Approach to Simulate Self-Assembly

   https://doi.org/10.1103/PhysRevX.14.041063  

   Trubiano, Anthony; Hagan, Michael F (December 2024, Physical Review X)

   Computational modeling of assembly is challenging for many systems, because their timescales can vastly exceed those accessible to simulations. This article describes the multiMSM, which is a general framework that uses Markov state models (MSMs) to enable simulating self-assembly and self-organization of finite-sized structures on timescales that are orders of magnitude longer than those accessible to brute-force dynamics simulations. As with traditional MSM approaches, the method efficiently overcomes free energy barriers and other dynamical bottlenecks. In contrast to previous MSM approaches to simulating assembly, the framework describes simultaneous assembly of many clusters and the consequent depletion of free subunits or other small oligomers. The algorithm accounts for changes in transition rates as concentrations of monomers and intermediates evolve over the course of the reaction. Using two model systems, we show that the multiMSM accurately predicts the concentrations of the full ensemble of intermediates on timescales required to reach equilibrium. Importantly, after constructing a multiMSM for one system concentration, yields at other concentrations can be approximately calculated without any further sampling. This capability allows for orders of magnitude additional speedup. In addition, the method enables highly efficient calculation of quantities such as free energy profiles, nucleation timescales, flux along the ensemble of assembly pathways, and entropy production rates. Identifying contributions of individual transitions to entropy production rates reveals sources of kinetic traps. The method is broadly applicable to systems with equilibrium or nonequilibrium dynamics and is trivially parallelizable and, thus, highly scalable. Published by the American Physical Society2024 

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4. Non-equilibrium early-warning signals for critical transitions in ecological systems

   https://doi.org/10.1073/pnas.2218663120  

   Xu, Li; Patterson, Denis; Levin, Simon Asher; Wang, Jin (January 2023, Proceedings of the National Academy of Sciences)

   Complex systems can exhibit sudden transitions or regime shifts from one stable state to another, typically referred to as critical transitions. It becomes a great challenge to identify a robust warning sufficiently early that action can be taken to avert a regime shift. We employ landscape-flux theory from nonequilibrium statistical mechanics as a general framework to quantify the global stability of ecological systems and provide warning signals for critical transitions. We quantify the average flux as the nonequilibrium driving force and the dynamical origin of the nonequilibrium transition while the entropy production rate as the nonequilibrium thermodynamic cost and thermodynamic origin of the nonequilibrium transition. Average flux, entropy production, nonequilibrium free energy, and time irreversibility quantified by the difference in cross-correlation functions forward and backward in time can serve as early warning signals for critical transitions much earlier than other conventional predictors. We utilize a classical shallow lake model as an exemplar for our early warning prediction. Our proposed method is general and can be readily applied to assess the resilience of many other ecological systems. The early warning signals proposed here can potentially predict critical transitions earlier than established methods and perhaps even sufficiently early to avert catastrophic shifts. 

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5. On the Generalization Ability of Coarse-Grained Molecular Dynamics Models for Nonequilibrium Processes

   https://doi.org/10.1137/24M1694549  

   Lyu, Liyao; Lei, Huan (June 2025, Multiscale Modeling & Simulation)

   One essential goal of constructing coarse-grained molecular dynamics (CGMD) models is to accurately predict nonequilibrium processes beyond the atomistic scale. While a CG model can be constructed by projecting the full dynamics onto a set of resolved variables, the dynamics of the CG variables can recover the full dynamics only when the conditional distribution of the unresolved variables is close to the one associated with the particular projection operator. In particular, the model's applicability to various nonequilibrium processes is generally unwarranted due to the inconsistency in the conditional distribution. Here, we present a data-driven approach for constructing CGMD models that retain certain generalization ability for nonequilibrium processes. Unlike the conventional CG models based on preselected CG variables (e.g., the center of mass), the present CG model seeks a set of auxiliary CG variables similar to the time-lagged independent component analysis to maximize the velocity correlation. This effectively minimizes the entropy contribution of unresolved variables and ensures the distribution under a broad range of nonequilibrium conditions approaches the one under equilibrium. Numerical results of a polymer melt system demonstrate the significance of this broadly overlooked metric for the model's generalization ability, and the effectiveness of the present CG model for predicting the complex viscoelastic responses under various nonequilibrium flows. 

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