Temperature measures a system's energy distribution from "summary" of Thermodynamics and an Introduction to Thermostatistics by Herbert B. Callen
The concept that temperature measures a system's energy distribution is fundamental to understanding the behavior of physical systems. In thermodynamics, temperature is not simply a measure of how hot or cold something is, but rather a reflection of the distribution of energy within the system. When we say that a system has a certain temperature, what we are really saying is that the energy of the system is distributed in a particular way among its constituent particles. At a higher temperature, the energy is more evenly distributed among the particles, while at a lower temperature, the energy is more concentrated in certain particles. This concept is closely related to the idea of entropy, which is a measure of the disorder or random...
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