Talk:Quantum thermodynamics

The dawn of quantum theory was in 1900, not 1905

According to the article, "... the relation $E=h\nu$. This paper is the dawn of quantum theory."

This relation is due to Max Planck, which he published in 1900. Had it been due to Einstein, h would have been called Einstein's constant instead of Planck's constant. Attributing it to Einstein misrepresents the history of quantum theory.

Einstein's contribution was to claim that light is quantized. But that's not part of thermodynamics because it makes no mention of either temperature or statistical ensembles. A few weeks after his initial paper giving his law, Planck explained its physical basis in terms of thermal radiators consisting of oscillators with quantized energy, which is the basis for quantum thermodynamics. Although Planck never explained how he first came up with the law, a plausible explanation is that he noticed that the denominator in the Rayleigh-Jeans law equaled the second term in the Taylor expansion about zero of the exponential term $e^{\frac {hc}{\lambda kT}}$ in the denominator of Wien's distribution law. At low frequencies this term dominates subsequent terms and therefore by subtracting 1 from Wien's exponential denominator Planck obtained a single term that worked as in the Rayleigh-Jeans law at frequencies well below the Wien peak and as in Wien's law at frequencies well above the Wien peak where the denominator was so much greater than 1 that subtracting 1 made a negligible difference.

The ratio ${\frac {hc}{\lambda kT}}$ contains both the fundamental quantum mechanical expression in the numerator and Boltzmann's fundamental thermodynamical expression in the denominator, leaving no doubt that Planck's law is a law of quantum thermodynamics. Vaughan Pratt (talk) 04:33, 29 March 2020 (UTC)