Who first defined temperature $T$ such that $\frac{1}{T} = \frac{\delta S}{\delta U}$, and where and when?
It could not have been Thomson, right? He did not have an entropy concept. Clausius?
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One should look at work of Poincaré who has developed a good part of the mathematical apparatus of thermodynamics. – Jean Marie Becker Apr 14 '20 at 21:18
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Thermodynamic temperature is defined as pV = RT, where p is pressure, V is the Volume, R the ideal gas constant and T the temperature.
Clausius in "The Mechanical Theory of Heat: With Its Applications to the Steam-engine and ..." (1864 ?) first introduced the concept of entropy as the integral dQ/T = dS.
The form that you give came much later and is the statistical mechanics definition of temperature. When exactly it was first defined I can't say.
James Wilson
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