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In this paper we introduce a diagnostic for measuring the quantum-classicaldifference for open quantum systems, which is the normalized size of thequantum terms in the Master equation for Wigner function evolution. For adriven Duffing oscillator, this measure shows remarkably precise scaling overlong time-scales with the parameter $\zeta_0=\hbar^2/D$. We also see that,independent of $\zeta_0$ the dynamics follows a similar pattern. For small$\zeta_0$ all of our curves collapses to essentially a single curve when scaledby the maximum value of the quantum-classical difference. In both limits oflarge and small $\zeta_0$ we see a saturation effect in the size of thequantum-classical difference; that is, the instantaneous difference betweenquantum and classical evolutions cannot be either too small or too large.

Parameter scaling in a novel measure of quantum-classical difference for decohering chaotic systems