## 3 Results
### Bioaccessibility and Shelf-Life Study of the Functional Beverage  
The beverage containing apple juice (as the basis) and olive pomace oil nanoemulsion underwent in vitro digestion using the INFOGEST 2.0 protocol [10]. The results for lycopene bioaccessibility were markedly different compared to the nanoemulsion alone, with values of 6.2 \(\pm\) 1.8% for the beverage in contrast to 53.8 \(\pm\) 4.2% for the pure nanoemulsion. The reduction in lycopene bioaccessibility could be attributed to the dilution of the nanoemulsion with apple juice, which may have slowed down the solubilization of lycopene into mixed micelles due to its lower concentration in the overall sample. Additionally, apple juice is rich in fibers such as pectin, which can hinder lycopene incorporation into mixed micelles or restrict the activity of pancreatic enzymes, resulting in lower extraction of lycopene from lipid droplets [68]. In contrast, the TPC bioaccessibility and antioxidant activity in the beverage showed no statistically significant difference (\(p\) > 0.05) compared to the nanoemulsion values, with TPC bioaccessibility at 119.1 \(\pm\) 5.7% for the beverage and 109.0 \(\pm\) 2.5% for the nanoemulsion, and antioxidant capacity at 62.0 \(\pm\) 3.5% compared to 63.6 \(\pm\) 2.3%, respectively. For an aseptically packaged lycopene-fortified apple juice beverage the considerations for shelf-life stability extend beyond microbiological safety to include the stability of the emulsion and the preservation of bioactive compounds. The overall shelf life is also influenced by factors such as the stability of the emulsion, lycopene degradation, and changes in sensory attributes. Similarly to the nanoemulsion lycopene stability, the degradation of lycopene in the functional beverage followed first-order kinetics (Figure 6) as a function of time and temperature, as observed in similar studies [49; 50]. The functional beverage enriched with lycopene and phenolic compounds was proven to be a stable system. Specifically, the phenolic compound concentration remained stable during storage, with no significant differences among storage temperature, as the TPC at the end of storage was 0.30 mg GAE/mL beverage and 0.33 mg GAE/mL beverage at 4 \({}^{\circ}\)C and 40 \({}^{\circ}\)C, respectively. However, lycopene appeared to be more prone to deterioration, as increased storage temperature led to higher degradation rates: \(-\)0.0088 d\({}^{-1}\) at 4 \({}^{\circ}\)C and \(-\)0.105 d\({}^{-1}\) at 40 \({}^{\circ}\)C (Figure 6). The initial concentration of lycopene was reduced by 32% after 47 days at 4 \({}^{\circ}\)C and by 53% after 19 days at 25 \({}^{\circ}\)C. Taking into consideration the degradation rates, lycopene in the functional beverage can be protected for longer storage periods at 4 and 10 \({}^{\circ}\)C. The functional properties of the proposed beverage are depended on lycopene content; thus, the shelf life of the product is determined by the point at which a 50% reduction in lycopene was observed. The estimated activation energy (Ea) was calculated to be 50.68 kJ/mol, which is a relatively moderate value. This implies that lycopene degradation is temperature-sensitive, meaning that small increases in temperature can lead to significantly faster degradation, yet it does not require high energy levels to occur. This observation aligns with the estimated shelf life (t\({}_{50}\)), which is 165 days at 4 \({}^{\circ}\)C, 103 days at 10 \({}^{\circ}\)C, 35 days at 25 \({}^{\circ}\)C, and 13 days at 40 \({}^{\circ}\)C, highlighting the importance of low-temperature storage to preserve the beverage's lycopene content and functional properties. Emulsions are inherently sensitive to destabilization mechanisms like creaming, flocculation, and coalescence, which can be accelerated by variations in temperature or pH. Therefore, maintaining the physicochemical stability of the lycopene emulsion is critical to ensuring the product's consistency, appearance, and nutritional quality.