Nonadiabaticity of quantum harmonic oscillators

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