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Abstract

For an FLRW model, thermodynamic phase transitions are investigated in the Einstein-Gauss-Bonnet gravity framework. Using the work density, the equation of state is derived, and the criticality conditions are employed to determine the critical points where possible phase transitions occur. The appearance of phase transitions strongly depends on the space-time dimension $n$. In this concern, for $n=5$, there is an ``inverted'' first-order phase transition, where the Gibbs free energy presents a swallow-tail behavior. On the other hand, for $n=6$, the system does not exhibit first order phase transition. In such a case, the Gibbs free energy presents a cusp with stable and unstable branches. For the present study, the mentioned phenomena are present for an expanding cosmology, where the matter distribution filling the Universe corresponds to a speculative matter distribution with an equation of state parameter greater than one. Interestingly, there are no phase transitions for dimensions greater than $n=6$, nor for expanding or contracting cosmological scenarios. To gain more insights into the system, the microstructure is analyzed using thermodynamic geometry to quantify the normalized scalar curvature. This invariant shows that an attractive interaction dominates the phase-transition region. Additionally, the topological thermodynamic analysis was performed employing Duan's off-shell map. This study reveals that for $n=5$ we observe a winding number interchange twice, indicating an unstable small/large branch phase transition through an intermediate stable phase. For $n=6$ the number of exotic defects is one. Consequently, we observe a stable small branch and an unstable large branch.