The levels of amygdalin and prunasin/sambunigrin were almost equal in Ozone but in Ozark, prunasin/sambunigrin levels were much higher than amygdalin . These concentrations are much higher than the levels found in the present study, as raw blue elderberry juice had a total CNG concentration of only 0.737 µg g-1 . Because CNGs are formed from phenylalanine, it is possible that the blue elderberry had limited stock of this key material to create CNGs. An alternative reason may be that blue elderberry may have less expression of the genes needed to form CNGs like sweet almonds compared to bitter almonds. CNGs may have also been degraded during juice preparation due to native β-glucosidases. A future study should investigate the impact of freezethaw cycles on the activity of β-glucosidase in elderberries because elderberries are frequently frozen before processing because they can spoil quickly if only refrigerated.Two cooking temperatures were investigated to understand the impact of temperature on the degradation rates of the phenolic compounds in blue elderberry juice. The pH and soluble solids were evaluated for the five juice replicates to ensure the juices were similar for the cooking process. The average pH value of the juices was 3.76 ± 0.11 and the average Brix reading was 16.2 ± 1.1%. The major phenolic compounds in elderberry juice were measured via HPLC-DAD and include 5-hydroxyprogallol hexoside , which is a novel phenolic compound tentatively identified for the first time by Uhl et al. 202239 chlorogenic acid, rutin, isorhamnetin-3-O-glucoside, cyn 3-sam, and cyn 3-glu. Whereas levels of cyn 3-sam and cyn 3-glu decreased to 82.2 ± 6.9 % and 79.3 ± 6.3 %, respectively , drainage planter pot more than 98% of the original concentration of 5-HPG, rutin, isorhamnetin-3-O-glucoside and chlorogenic acid remained after two hours.
At the higher cooking temperature , the anthocyanins again experienced significant degradation, retaining only 33.2 ± 4.6 % and 36.8 ± 5.5 % of the original concentration after cooking two hours . In a separate study of the thermal stability of elderberry juice, 15% of cyn 3-sam and cyn 3-glu were retained in juice as compared to control juice.1 Szalóki-Dorkó, et al. demonstrated that the more complexly glycosylated anthocyanins cyn 3-sam is more stable during thermal process as compared to cyn 3-glu. The results of our study are similar to Oancea et al. which showed after 90 min at 100 °C, total anthocyanin content degraded 58 %.58 However, that study also observed an increase in total phenolic and total flavonoid content after 60 min, followed by a gradual decrease, which was not observed herein. If sample vials were sealed well to protect from any loss of moisture, this increase in concentrations may be due to the release of phenolic compounds bound to the cell well or other polysaccharides, which can be released with the assistance of pectinase treatments. Because elderberry has predominantly cyanidin-based anthocyanins, protocatechuic acid is typically found as the main degradation product, though phloroglucinaldehyde can also be formed. However, neither protocatechuic acid nor phloroglucinaldehyde were observed in any of the cooked juice samples. Protocatechuic acid dihexoside, which was tentatively identified in an earlier study of blue elderberry did not increase over the cooking period. Caffeic acid, a hydroxycinnamic acid increased up to 108.1% of its initial concentration after 2 hours of cooking at 72 °C, and up to 147.1% after 2 hours of cooking at 95 °C. The levelsof caffeic acid were highly variable, with larger standard deviations that the other phenolic compounds. This is a known metabolite of cyanidin-based anthocyanins,and further work investigating the breakdown of anthocyanins in blue elderberry juice into this phenolic acid can elucidate the pathway to this compound.
The main flavonols in blue elderberry, rutin and isorhamnetin glucoside, were stable during the thermal processing, retaining 100.5% and 99.3%, respectively, of their original concentration even at 95 °C . The high retention rates of rutin and isorhamnetin glucoside match literature reports for the thermal stability of these compounds, which show that rutin has a strong thermal stability at acidic pH. More than 80% of the starting concentration was retained after five hours of cooking at 100 °C at pH 5. Our results do not agree with another study in which rutin had an activation energy 107.3 kJ/mol, and the half-life values at 70 and 90 °C were 19.25 and 1.99 h, respectively; however, the rutin was in an aqueous solution at pH 6.6. Other compounds present in blue elderberry juice, in addition to a lower pH, could cause synergistic effects to improve stability of rutin in the present study. Limited information on the thermal stability of isorhamnetin glucoside was found, though a study of black currant juice stability found that during long-term storage at room temperature and at 4 °C, isorhamnetin glucoside concentrations did not change significantly during the 12-month period. In the same study, rutin did not change significantly during storage. The main phenolic acid in blue elderberry juice, chlorogenic acid, was also thermally stable. This result was unexpected, as another study on the thermal stability of chlorogenic acid in a complex with amylose showed a significant decrease in content after 10-15 minutes, depending on the temperature. Their results also showed that a 10 °C increase in temperature results in a 2.5-fold increase in the rate of degradation of chlorogenic acid. It can be beneficial to maintainlevels of chlorogenic acid in anthocyanin-rich matrices, as shown in black carrot extract where chlorogenic acid increased absorbance of cyanidin-based anthocyanins at pH 3.6 and 4.6 due to intermolecular co-pigmentation.
Overall, our results show that blue elderberry juice behaves similarly to anthocyanin-rich matrices, in that longer processing at higher temperatures degrades anthocyanins. The two main anthocyanins in blue elderberry, cyn 3-sam and cyn 3-glu, behaves similarly during processing, degrading at about the same rate at 72 °C and 95 °C. Furthermore, the other major phenolic compounds like rutin, isorhamnetin, and chlorogenic acid, were highly stable and can withstand the thermal processing. Our study into the effects of thermal processing on the phenolic composition and cyanogenic glycoside content in blue elderberry juice showed that the main anthocyanins present degrade faster at higher temperatures but other important phenolic compounds like rutin and isorhamnetin 3-glucoside are more thermally stable, retaining over 90% of their original concentrations even after two hours at 95 °C. Furthermore, neoamygdalin and sambunigrin were measured in the blue elderberry juice, which were in lower concentrations compared to European and American elderberry.The Berry phase has played significant roles in many aspects of physics, ranging from atoms to molecules to condensed-matter systems. As pointed out in Ref., the Berry phase has a profound geometrical origin because an adiabatic and cyclic process of a quantum state is mathematically equivalent to parallel transporting it along a loop, which connects to the concept of holonomy in geometry. Hence, the Berry phase bridges physics and geometry, making it extremely important in the understanding of topological phenomena, such as integer quantum Hall effect, topological insulators and superconductors, and others. The description of the Berry phase relies on the properties of a pure state of a quantum systems at zero temperature. Meanwhile, mixed quantum states, including thermal state at finite temperatures, are more common. Therefore, mixed-state generalizations of the Berry phase have been an important task. Uhlmann made a breakthrough by constructing the Uhlmann connection for exploring the topology of finite-temperature systems. As the Berry holonomy arises from paralleltransport of a state-vector along a closed path, the Uhlmann holonomy is generated by parallel-transporting the amplitude of a density matrix. defined by W = √ρU. Here the amplitude W is the mixed-state counterpart of the wave function, and U is a phase factor. A geometrical phase is deduced from the initial and final amplitudes. However, Uhlmann’s definition of parallel transport is rather abstract and may involve nonunitary processes, complicating a direct and clear physical interpretation. Moreover, plant pot with drainage the fiber bundle built upon Uhlmann’s formalism is trivial, which severely restricts its applications in physical systems.Purification of a mixed state leads to purified state, a state-vector equivalent to the amplitude of a density matrix. The lack of a one-to-one correspondence between the density matrix and its purified states gives rise to a phase factor, similar to the phase of a wave function. In a branch of quantum field theory called thermal field theory, there is a similar structure for describing the thermal-equilibrium state of a system by constructing the corresponding thermal vacuum by duplicating the system state as an ancilla and forming a composite state. It plays a crucial role in the formalism of traversable wormholes induced by the holographic correspondence between a quantum field theory and a gravitational theory of one higher dimensions. Importantly, purified states of a two level system has been demonstrated on the IBM quantum computer while the thermal vacuum of a transverse field Ising model in its approximate form has been realized on a trapped-ion quantum computer. Despite the superficial similarity, a major difference between a thermal vacuum and a purified state is a partial transposition of the ancilla to ensure the Hilbert-Schmidt product is well defined.
In quantum information theory, a partial transposition is closely related to entanglement of mixed states. Importantly, partial transpositions of composite systems have been approximately realized in experiments by utilizing structural physical approximations in suitable quantum computing platforms. Although ordinary observables cannot discern the partial transposition between the purified state and thermal vacuum, here we will show that at least two types of generalizations of the Berry phase to mixed states are capable of differentiating the two representations of finite temperature systems. Among many attempts to generalize the Berry phase or related geometric concepts to mixed states, a frequently mentioned approach was proposed in Ref. Instead of decomposing the density matrix to obtain a matrix-valued phase factor, a geometrical phase is di-rectly assigned to a mixed state after parallel transport by an analogue of the optical process of the MachZehnder interferometer. Hence, the geometrical phase generated in this way is often referred to as the interferometric phase. The interferometric phase has been generalized to nonunitary processes, but the transformations are still on the system only. Moreover, it is essentially different from Uhlmann’s theory since the conceptual structure of holonomy is not incorporated. We will first derive a mixed-state generalization of the parallel-transport condition for generalizing the Berry phase without invoking holonomy. This approach unifies the necessary condition for both the interferometric phase and Uhlmann phase . Two ways to implement the parallel-transport condition based on how the system of interest undergoes adiabatic evolution will be introduced, and they lead to different generalizations of the Berry phase. We will name one thermal Berry phase and the other generalized Berry phase. Importantly, the partial transposition of the ancilla between a purified state and thermal vacuum will be shown to produces observable geometrical effects in both thermal Berry phase and generalized Berry phase. Through explicit examples, the two generalized phases are shown to differentiate the two finite-temperature representations, a task beyond the capability of the conventional interferometric phase or Uhlmann phase. The rest of the paper is organized as follows. Sec. II summarizes the Berry phase in a geometrical framework with an introduction of the parallel-transport condition for pure quantum states. In Sec. III, we review the representations of mixed states via purified states and thermal vacua and then explain the difference of the partial transposition of the ancilla. In Sec. IV, we introduce the thermal Berry phase via generalized adiabatic processes. While the thermal Berry phase can differentiate a purified state from a thermal vacuum, it may contain non-geometrical contributions. In Sec. V, we generalize the parallel-transport condition to involve the system and ancilla and derive the general Berry phase according to the generalized condition. While the generalized Berry phase only carries geometrical information, its ability of differentiating a purified state from a thermal vacuum depends on the setup and protocol. We present examples of the thermal and generalized Berry phases. Sec. VI concludes our study. Some details and derivations are given in the Appendix.While purified states of a two-level system incorporating environmental effects have been simulated on the IBM quantum platform, thermal vacua of the transverse Ising model has been experimentally realized on an ion-trap quantum computer by the quantum approximate optimization algorithm. Moreover, partial transposition of a composite system has been approximately realized on quantum computers with various numbers of qubits.