The concept of entropy has undergone a radical evolution, transitioning from a localized observation of thermal inefficiency in 19th-century steam engines to a universal metric of uncertainty, structural complexity, and informational distribution across a multitude of disciplines.

In classical thermodynamics, Rudolf Clausius introduced entropy to quantify heat transfer and the inevitable increase of disorder in physical systems. Ludwig Boltzmann later redefined it in statistical mechanics as a measure of the number of possible microstates compatible with a given macrostate. Claude Shannon extended this concept into information theory, defining entropy as the average level of "missing information," uncertainty, or "surprise" in a message. The conceptual gap between physical and informational entropy was successfully bridged by Landauer's Pri ...