Probabilistic dynamics operators for path-entropy-guided nonequilibrium control of self-assembly
Abstract
Self-assembly is inherently dynamical, with competing pathways, metastable intermediates, and kinetic traps influencing which structures ultimately form. The resulting dynamics can be irreversible and generate entropy, providing potentially useful information about how a system progresses toward an assembled state. However, data-driven approaches for controlling self-assembly commonly optimize structural observables that provide limited information about these nonequilibrium dynamics. Here, we introduce a probabilistic dynamics operator (PDO) that learns the time evolution of probability distributions in a reduced collective variable space. The learned operator provides both an efficient dynamical surrogate compared to molecular dynamics (MD) simulations and access to probability fluxes from which entropy production can be quantified. We validate the PDO using discrete Markov ring and continuous triple-well systems and show that models trained exclusively on fixed-temperature trajectories also predict dynamics and accumulated entropy production under unseen, time-varying temperature protocols. We then apply the PDO to patchy particles that competitively assemble into rhombohedral () and trihexagonal morphologies, using the PDO as a surrogate environment for reinforcement learning of temperature protocols. A -morphology-only objective produces yields of 62% comparable to the best fixed-temperature MD simulations, whereas augmenting the objective with a moderate contribution from excess entropy production substantially increases formation to 90% in explicit MD simulations. The optimal temperature control policy exploits transient melting and reorganization before promoting renewed growth, while excessive weighting of entropy production suppresses assembly. These results demonstrate that path entropy-dependent thermodynamic information can provide a useful signal for controlling self-assembly when productive pathways require nonequilibrium reorganization.
Related
- Information Entropy and Dissipation Potential in Stochastic Nambu Nonequilibrium Thermodynamics
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- Reversibility of Nonequilibrium Dynamics in a Unitary Fermi Gas
- Nonequilibrium Quasiparticle Effects on Domain Wall Dynamics in Superconductors
BibTeX
@misc{paul2026probabilistic,
title = {{Probabilistic dynamics operators for path-entropy-guided nonequilibrium control of self-assembly}},
author = {Sanjib Paul and Anna Wojnar and Xun Tang and Alexander J. Pak},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15008400/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008400/v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - Probabilistic dynamics operators for path-entropy-guided nonequilibrium control of self-assembly
AU - Sanjib Paul
AU - Anna Wojnar
AU - Xun Tang
AU - Alexander J. Pak
PY - 2026
DA - 2026/09/07
PB - ChemRxiv
DO - 10.26434/chemrxiv.15008400/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008400/v1
AB - Self-assembly is inherently dynamical, with competing pathways, metastable intermediates, and kinetic traps influencing which structures ultimately form. The resulting dynamics can be irreversible and generate entropy, providing potentially useful information about how a system progresses toward an assembled state. However, data-driven approaches for controlling self-assembly commonly optimize structural observables that provide limited information about these nonequilibrium dynamics. Here, we introduce a probabilistic dynamics operator (PDO) that learns the time evolution of probability distributions in a reduced collective variable space. The learned operator provides both an efficient dynamical surrogate compared to molecular dynamics (MD) simulations and access to probability fluxes from which entropy production can be quantified. We validate the PDO using discrete Markov ring and continuous triple-well systems and show that models trained exclusively on fixed-temperature trajectories also predict dynamics and accumulated entropy production under unseen, time-varying temperature protocols. We then apply the PDO to patchy particles that competitively assemble into rhombohedral () and trihexagonal morphologies, using the PDO as a surrogate environment for reinforcement learning of temperature protocols. A -morphology-only objective produces yields of 62% comparable to the best fixed-temperature MD simulations, whereas augmenting the objective with a moderate contribution from excess entropy production substantially increases formation to 90% in explicit MD simulations. The optimal temperature control policy exploits transient melting and reorganization before promoting renewed growth, while excessive weighting of entropy production suppresses assembly. These results demonstrate that path entropy-dependent thermodynamic information can provide a useful signal for controlling self-assembly when productive pathways require nonequilibrium reorganization.
ER -