(330i) Temperature-Transferable Coarse-Grained Modeling with Relative Entropy

Systematic methods for bottom-up coarse-graining are essential tools for developing accurate multiscale models of complex systems. Relative entropy optimization can produce coarse-grained models that accurately capture interactions at a given set of thermodynamic conditions. However, such approaches can suffer issues related to the transferability and representability problems in coarse-graining. For example, coarse interactions appropriate for one temperature might lead to inaccurate behavior at another, while thermodynamic properties including energy might be incorrectly predicted even when structure is reproduced properly. These shortcomings are fundamental to systematic coarse-graining approaches that treat coarse force fields in terms of fixed potentials rather than temperature-dependent interaction free energies. As strong temperature-dependent behavior is a hallmark of many fluid and polymer systems of interest for multiscale modeling, inaccurate prediction of such dependence remains a critical problem for coarse-graining in general.

Here, we present a novel approach to resolving this temperature transferability problem with an extension of the relative entropy coarse-graining method based on joint probability distributions of configurations and energies. In this approach, relative entropy minimization at a single temperature allows rigorous decomposition of a coarse-grained potential of mean force into temperature-dependent energetic and entropic components. The resulting coarse-grained model can then be used to calculate an effective force field at any temperature. Furthermore, it can predict the distribution of energies in the underlying detailed system, and its temperature dependence, for the entire ensemble of possible coarse-grained configurations. We demonstrate our method here with a variety of systems including model fluids and molecular systems such as alkanes and water. Using atomistic simulations of these systems at only single temperatures, our method is able to predict configurational and energetic probability distributions over a range of temperatures. In the end, this systematic approach to temperature transferability and related representability issues stands in contrast to other ad hoc solutions to these problems, and has the potential to expand the range of systems that can be studied readily with coarse-grained models.