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We employ a statistical approach to investigate the influence of axialasymmetry on the nuclear level density and entropy along the fission pathwaysof a superheavy nucleus, explicitly focusing on the $^{296}$Lv isotope. Thesepathways are determined within multidimensional deformation spaces. Ouranalysis reveals a significant impact of triaxiality on entropy. Additionally,suppressing shell effects can alter the fission scenario depending on theavailable excitation energy. We derive the deformation-dependent level densityparameter, which plays a crucial role in estimating the survival probability ofa superheavy nucleus. Furthermore, we utilize a set of master equations toobtain the time-dependent fission probabilities and calculate the ratio ofdecay probabilities for both axial and triaxial paths.

Entropies, level-density parameters, and fission probabilities along the triaxially- and axially-symmetric fission paths in $^{296}$Lv