Symmetric cumulants can improve our understanding of the joint probability distribution function $P(v_m,v_n,v_k,\cdots ,{\mathrm{\Psi }}_m,{\mathrm{\Psi }}_n,{\mathrm{\Psi }}_k,\cdots )$, potentially offering new insights into the nature of the fluctuations of the quark-gluon plasma produced in relativistic heavy-ion collisions. In this work, the four-particle symmetric cumulants $s{c}_{2,3}\left\{4\right\}$, six-particle symmetric cumulants $s{c}_{2,3,4}\left\{6\right\}$, and the normalized cumulants $ns{c}_{2,3}\left\{4\right\}$ and $ns{c}_{2,3,4}\left\{6\right\}$ originating from transverse momentum conservation, collective flow, and the interplay between the two effects are calculated. Our results on $s{c}_{2,3}\left\{4\right\}$ are consistent with the ATLAS data using the subevent cumulant method, facilitating a more profound understanding of the origins of the symmetric cumulant in small systems. Our results on $s{c}_{2,3,4}\left\{6\right\}$ serve as theoretical predictions for future experimental measurements in small systems.

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• Collective flow
• Collective models
• Quark-gluon plasma