A microscopic view of heat exchanges: Born's contribution to the demonstration od Boltzmann Principle

The heat $delta Q$ was the conundrum of the ancient age of Thermodynamics, until Boltzmann's H-theorem and Botzmann Principle (BP) $S=kappa ln W$, made it possible to express the entropy in terms of the number $W$ of available states. At this stage, the Second Principle $delta Q=TdS$ could be used to calculate the heat, even in the absence of a clear relationship between what Thermodynamics calls "heat exchange" and the forces acting at a microscopic level. We recover Max Born's definition of heat exchange, as the mechanism that modifies the energy levels' populations. From this definition, BP can be demonstrated, without recursion to the H-theorem, as shown by Born itself. Dragging to the light Born's contribute to Statistical Thermodynamics, modestly relegated by the Author to a textbook appendix, is the main aim of the present note. The second one is showing that Born's definition of heat exchange follows from the notion of generalized scattering process.