We present, for the first time, simultaneous determination of shear viscosity ($eta$) and entropy density ($s$) and thus, $eta/s$ for equilibrated nuclear systems from $A$ $sim$ 30 to $A$ $sim$ 208 at different temperatures. At finite temperature, $eta$ is estimated by utilizing the $gamma$ decay of the isovector giant dipole resonance populated via fusion evaporation reaction, while $s$ is evaluated from the nuclear level density parameter (${a}$) and nuclear temperature ($T$), determined precisely by the simultaneous measurements of the evaporated neutron energy spectra and the compound nuclear angular momenta. The transport parameter $eta$ and the thermodynamic parameter $s$ both increase with temperature resulting in a mild decrease of $eta$/$s$ with temperature. The extracted $eta$/$s$ is also found to be independent of the neutron-proton asymmetry at a given temperature. Interestingly, the measured $eta$/$s$ values are comparable to that of the high-temperature quark-gluon plasma, pointing towards the fact that strong fluidity may be the universal feature of the strong interaction of many-body quantum systems.
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