A new mathematical tool from Penn engineers, called Stochastic Thermodynamics with Internal Variables (STIV), helps predict how tiny movements of atoms and molecules lead to bigger changes, like proteins folding, crystals forming, or ice melting.
This tool avoids the need for slow and expensive experiments or simulations. It could improve the design of medicines, semiconductors, and other materials by making predictions faster and more accurate. The research, published in Journal of the Mechanics and Physics of Solids, used STIV to solve a 40-year-old problem in phase-field modeling. Phase-field modeling is a method to study the boundary where two states of matter meet, like the edge between water and ice or folded and unfolded parts of a protein. STIV uses basic principles to describe how these boundaries change, without relying on experimental data.
How the tool functions
The STIV framework builds on ideas from French physicist Paul Langevin, who developed ways to describe how atoms and molecules move in environments that are always changing. STIV uses internal variables to capture how a system behaves when it’s not in equilibrium. Choosing the right variables is key, similar to how the Rosetta Stone used Greek and Demotic text to decode hieroglyphs.
With the right variables, STIV can predict how a system evolves without constant adjustments. A second paper published in Journal of Non-Equilibrium Thermodynamics expanded STIV to work for many different situations. This update included three methods: two are fast and cover most cases, while the third is slower but handles rare scenarios. These methods make STIV practical and widely usable. Unlike older methods that were either slow and accurate or fast but less precise, STIV offers both speed and accuracy. It has already helped researchers in the U.S. and Italy study how biological cells move. By providing a common approach for different problems, STIV could lead to new discoveries in fields like biology, materials science, and engineering.