Nonadiabaticity of Quantum harmonic oscillators

We propose a quantity, ${\mathcal{A}\!\!\!/}$, as a measure describing the nonadiabaticity of a thermodynamic process. For this purpose, we use a schematic method to find the measure of the `degree of nonadiabaticity'. The method utilizes an `invariant' thermal state constructed from the Ermakov-Lewis-Riesenfeld invariant. Specifically, we study a frequency-modulated quantum harmonic oscillator as a thermodynamic system. Naturally, we write the first law of thermodynamics with ${\mathcal{A}\!\!\!/}$ as a measurable quantity. We discuss universality for the method and some possible applications.