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Active glassy systems can be thought of as simple model systems that imitatecomplex biological systems. Sometimes, it becomes crucial to estimate theamount of the activity present in such biological systems, such as predictingthe progression rate of the cancer cells or the healing time of the wound. Inthis work, we study a model active glassy system to understand a possiblequantification of the degree of activity from the collective, long-range phononresponse in the system. We find that the four-point dynamic susceptibility,$\chi_4(t)$ at the phonon timescale, grows with increased activity. We thenshow how one can estimate the degree of the activity at such a small timescaleby measuring the growth of $\chi_4(t)$ with changing activity. A detailedfinite size analysis of this measurement, shows that the peak height of$\chi_4(t)$ at this phonon timescale increases strongly with increasing systemsize suggesting a possible existence of an intrinsic dynamic length scale thatgrows with increasing activity. Finally, we show that this peak height is aunique function of effective activity across all system sizes, serving as apossible parameter for characterizing the degree of activity in a system.

Enhanced Phonon Peak in Four-point Dynamic Susceptibility in the Supercooled Active Glass-forming Liquids