## 3 Results and Discussion  
Fractionation has been shown to enhance the activity of EOs by exerting bactericidal effects and interfering with microbial resistance and virulence mechanisms, providing a multifaceted approach to microbial control [64]. The MBC, defined as the lowest concentration at which no microbial growth was observed across all replicates and repetitions, was 2.00 \(\pm\) 0.00% \(\sigma/v\) for PEO. In contrast, FIV exhibited a significantly lower MBC of 0.10 \(\pm\) 0.00% \(v/v\) (\(p<0.05\)), indicating an enhanced antibacterial effect. To better simulate sublethal conditions for subsequent thermal treatments, the SLC was determined as the highest concentration at which no significant inhibition of bacterial growth occurred. The SLC values were 0.13 \(\pm\) 0.00% for PEO and 0.09 \(\pm\) 0.05% for FIV. However, in practice, using the full SLC values during combined treatments led to unexpectedly rapid bacterial inactivation, which hindered reliable colony enumeration. Therefore, to preserve the concept of a mild stress hurdle while still enabling measurable survival during the thermal treatments, it was selected as 0.06% for both PEO and FIV, which are concentrations below the experimentally determined SLCs. This adjustment allowed the OEOs to act as sublethal stressors rather than primary inactivating agents. The selected concentrations are consistent with previous reports on subinhibitory levels of OEO capable of enhancing microbial susceptibility to additional hurdles without achieving complete inactivation [65,66]. Figure 1 shows the inactivation curves of \(L\). _monocytogenes_ (\(\log\text{N}/\text{N}_{0}\) versus time) at 52, 54, 57.5, and 63 \({}^{\circ}\)C in the SMM. The treatments with PEO and FIV resulted in more pronounced initial reductions compared to the control. The inactivation data were fitted using both the Weibull-Mafart and Bigelow models (Table 1). Although both models showed low RMSE values, the Weibull-Mafart model provided a better fit, with lower RMSE and AIC and A\({}_{f}\)/B\({}_{f}\) values closer to one. Therefore, this model was selected to estimate thermal inactivation parameters. The Weibull-Mafart model estimates the \(\delta\)-value, representing the time to achieve one logarithm reduction in the microbial population under a specific temperature, which is equivalent to the D-value (min) [52]. Table 2 summarizes the estimated \(\delta\)-values (min) of \(L\). _monocytogenes_ for each group at the four temperatures evaluated. As expected, \(\delta\)-values decreased with increasing temperature. Across all temperatures, FIV exhibited consistently lower \(\delta\)-values than the control, with non-overlapping confidence intervals, suggesting a meaningful difference. PEO also showed lower \(\delta\)-values compared to the control at 52 and 63 \({}^{\circ}\)C. At 54 and 57.5 \({}^{\circ}\)C, the \(\delta\)-values estimates for PEO and FIV were closer in magnitude, but some separation between their confidence intervals was still observed. The higher inactivation observed with FIV may be attributed to its higher concentrations of carvacrol and thymol, which are known to exert strong antimicrobial