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A thermodynamic process is a solution of the balance equations fulfilling the second law of thermodynamics. This implies restrictions on the constitutive relations. The most general way to exploit these restrictions is the method introduced by Liu. This method is applied here, in contrast to most of the literature on relativistic thermodynamic constitutive theory, which goes back to a relativistic extension of the Thermodynamics of Irreversible Processes. In the present work, the balance equations and the entropy inequality are formulated in the special relativistic four-dimensional form for an observer with four-velocity parallel to the particle current. The restrictions on constitutive functions are exploited in the relativistic formulation. The domain of the constitutive functions, the state space, is chosen to include the particle number density, the internal energy density, the space derivatives of these quantities, and the space derivative of the material velocity for a chosen observer. The resulting restrictions on constitutive functions, as well as the resulting entropy production are investigated in the non-relativistic limit, and relativistic correction terms of the lowest order are derived. The restrictions on constitutive functions and the entropy production in the low energy limit are compared to the results of an exploitation of the non-relativistic balance equations and entropy inequality. In the next order of approximation our results are compared to the Thermodynamics of Irreversible Processes. Full article

Biofouling attaches to immersed surfaces in between hull cleanings. Due to high speeds and relatively short port times, biofilm often attaches to the immersed surfaces of containerships. In most cases, this type of fouling is not given much importance since it is assumed that it will not cause any fouling penalties. In this paper, the fouling penalties related to fouling with biofilm on the example of the Post Panamax and Post Panamax Plus containership fleets sailing in the Adriatic Sea are assessed. In addition, the investigation is performed for real environmental conditions that a containership can encounter on a sailing route passing through the Adriatic Sea. Thus, the impact of waves and wind is taken into account based on mean values of significant wave height and wind speed for containerships sailing at the design speed along the analyzed route. The procedure for the determination of the detrimental effects of biofilm on the increase in fuel consumption and carbon dioxide emissions is given. Further, the proposed procedure includes the determination of calm water resistance by the Holtrop and Mennen method, the added resistance in waves by Liu and Papanikolaou’s method, spectral analysis using the Tabain’s spectrum for the Adriatic Sea, the wind resistance by the Blendermann method, and added resistance due to biofouling using the Granville method. Thereafter, a time-dependent biofouling growth model proposed by Uzun et al. is incorporated, and the adequate timing for underwater hull cleaning is determined for several hull cleaning costs. The obtained results demonstrate that, from an environmental point of view, proactive hull cleaning should be applied, while, from an economic perspective, optimal timing for underwater hull cleaning is recommended. Full article

Herein we study the problem of recovering a density operator from a set of compatible marginals, motivated by limitations of physical observations. Given that the set of compatible density operators is not singular, we adopt Jaynes’ principle and wish to characterize a compatible density operator with maximum entropy. We first show that comparing the entropy of compatible density operators is complete for the quantum computational complexity class QSZK, even for the simplest case of 3-chains. Then, we focus on the particular case of quantum Markov chains and trees and establish that for these cases, there exists a procedure polynomial in the number of subsystems that constructs the maximum entropy compatible density operator. Moreover, we extend the Chow–Liu algorithm to the same subclass of quantum states. Full article

Background: Commercial pharmaceutical herbal products have enabled people to take traditional Chinese medicine (TCM) in a convenient and accessible form. However, the quantity and quality should be additionally inspected. To address the issue, a combination of chemical and physical inspection methods were developed to evaluate the amount of an herbal formula, Xiang-Sha-Liu-Jun-Zi-Tang (XSLJZT), in clinical TCM practice. Methods: A high-performance liquid chromatography–tandem mass spectrometry (HPLC–MS) method with electrospray ionization was developed to measure the herbal biomarkers of guanosine, atractylenolide III, glycyrrhizic acid, dehydrocostus lactone, hesperidin, and oleanolic acid from XSLJZT. Scanning electron microscopy (SEM) photographs and light microscopy photographs with Congo red and iodine–KI staining were used to identify the cellulose fibers and starch content. Furthermore, solubility analysis, swelling power test, and crude fiber analysis were contributed to measure the starch additive in pharmaceutical products. Results: The results demonstrated large variations in the chemical components of different pharmaceutical brands. The SEM photographs revealed that the starch was oval, smooth, and granular, and that the raw herbal powder appears stripy, stretched, and filiform. The stained light microscopy photographs of all of the pharmaceutical products showed added starch and raw herbal powder as extenders. Conclusion: The developed chemical and physical methods provide a standard operating procedure for the quantity control of the herbal pharmaceutical products of XSLJZT. Full article