This talk will focus on my doctoral research and consists of two parts.

In the first part of the seminar, I will introduce my work on data-driven discovery of internal variables. Internal variable theory has been highly successful in continuum mechanics, but its reliance on phenomenological intuition—often without a direct connection to lower-scale structure—can lead to black-box models with uncertain applicability and limited generalizability. Inspired by recent developments in Stochastic Thermodynamics with Internal Variables (STIV), which provides a first-principles-based definition of internal variables, their dynamics, and thermodynamic quantities such as entropy and non-equilibrium free energy, we propose IB-VONNs: a data-driven framework for identifying internal variables as functions of microscopic degrees of freedom, along with the associated constitutive relations. Physical constraints and thermodynamic consistency are incorporated into the framework. We demonstrate the approach using a one-dimensional phase-transforming system governed by Langevin dynamics, and I will also discuss ongoing applications to the rheology of two-dimensional colloidal systems.

In the second part of the seminar, I will discuss my ongoing work on non-equilibrium entropy. A broad class of dynamical systems can be formulated within the framework of the General Equation for Non-Equilibrium Reversible–Irreversible Coupling (GENERIC), which is grounded in statistical mechanics. Building on this structure, we establish a general identity and an associated numerical method for computing non-equilibrium entropy differences from mesoscopic fluctuation data. This differs from well-established fluctuation theorems, such as the Jarzynski equality, which are primarily used to extract equilibrium free energy differences.