Unveiling Scale-Dependent Statistical Physics: Connecting Finite-Size and Non-Equilibrium Systems for New Insights

A scale-dependent effective temperature emerges as a unifying principle in the statistical physics of apparently different phenomena, namely quantum confinement in finite-size systems and non-equilibrium effects in thermodynamic systems. This concept effectively maps these inherently complex systems onto equilibrium states, thereby enabling the direct application of standard statistical physics methods. By offering a framework to analyze these systems as effectively at equilibrium, our approach provides powerful new tools that significantly expand the scope of the field. Just as the constant speed of light in Einstein's theory of special relativity necessitates a relative understanding of space and time, our fixed ratio of energy to temperature suggests a fundamental rescaling of both quantities that allows us to recognize shared patterns across diverse materials and situations.