How do materials deform and flow? Answering this question requires models that can capture inelastic, non-equilibrium behavior. While continuum mechanics has been remarkably successful in describing such phenomena, fundamental questions remain: How should internal variables, namely, the hidden state descriptors that encode a material’s microstructural history, be chosen? And what is the thermodynamic structure underlying their evolution?
This talk presents my doctoral research on attempts to address both questions by combining principles from statistical mechanics with modern machine learning techniques.

In the first part, I will introduce IB-VONNs, a data-driven framework for discovery of microstructure-based internal variables directly from microscopic data. Classical internal variable theory has been highly successful in continuum mechanics, yet it relies heavily on phenomenological intuition, often without a direct link to the underlying microstructure. Inspired by recent developments in Stochastic Thermodynamics with Internal Variables (STIV), which provides a first-principles foundation for internal variables, their dynamics, and associated thermodynamic quantities, IB-VONNs identifies internal variables as explicit, observable functions of microscopic degrees of freedom, together with thermodynamically consistent constitutive relations. The framework is demonstrated on a one-dimensional phase-transforming system and on the rheology of two-dimensional colloidal systems under oscillatory shear.

In the second part, I will present a new theoretical result and associated numerical method for computing non-equilibrium entropy differences. A broad class of physical systems can be formulated within the General Equation for Non-Equilibrium Reversible–Irreversible Coupling (GENERIC), a framework with strong statistical mechanics foundations and clear physical interpretation. Building on this structure, we establish a general identity for non-equilibrium entropy differences intrinsic to irreversible dynamics, a result that complements well-known fluctuation theorems such as the Jarzynski and Crooks equalities, which target equilibrium free-energy differences.

Together, these contributions provide a coherent set of tools for inelastic material modeling by bridging microscopic physics and continuum thermodynamics.