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In the branch of physics called [[statistical mechanics]], [[entropy]] is a measure of the randomness or disorder of a physical system. This concept was studied in the 1870s by the Austrian physicist [[Ludwig Boltzmann]], who showed that the [[thermodynamics|thermodynamic]] properties of a [[gas]] could be derived from the combined properties of its many constituent [[molecule]]s. Boltzmann argued that by averaging the behaviors of all the different molecules in a gas, one can understand macroscopic properties such as volume, temperature, and pressure. In addition, this perspective led him to give a precise definition of entropy as the [[natural logarithm]] of the number of different states of the molecules (also called ''microstates'') that give rise to the same macroscopic features.<ref>[[#Yau|Yau and Nadis]], pp. 187–188</ref>
In the twentieth century, physicists began to apply the same concepts to black holes. In most systems such as gases, the entropy scales with the volume. In the 1970s, the physicist [[Jacob Bekenstein]] suggested that the entropy of a black hole is instead proportional to the ''surface area'' of its [[event horizon]], the boundary beyond which matter and radiation
: <math>S= \frac{c^3kA}{4\hbar G}</math>
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