Quantifying `local softness' in a simple liquid

Mutual information between local stress and local non-affine deformation is proposed as a collective field variable quantifying the {\em local softness} of soft materials. The liquid-solid transition in a simple liquid is considered as a generic example of mechanical transformation through varying correlation between stress and deformation at the microscopic level. Probing through this new measure, a liquid appears as a spatially heterogeneous medium of interacting interconnected regions of varying softness. In contrast, the soft regions shrink to isolated spots in the background of a negligible mean softness in the case of solids. In this view, the thermodynamic transition becomes purely geometric while keeping the essential mechanical information intact. Besides offering a general framework for understanding the mechanics of materials, this new approach can complement recent machine learning efforts by assigning physical meaning to their findings. Further, this collective variable can be used on the fly during material characterization as both of its ingredient variables are experimentally accessible.