Quantum physics is intrinsically probabilistic. The entropy of a quantum state quantifies the amount of randomness (or information loss) of such state. The degrees of freedom of a quantum state are position and spin, and upon their specification Born's rule in phase space defines randomness. We focus on the spin degree of freedom and elucidate the spin entropy. Then, we present some of its properties and show how entanglement increases spin entropy. Some speculative predictions on the decay of the $Z^0,W^{+,-}$ gauge bosons conclude the paper.

We changed the symmetry of the Weak Force from SU(2) to the quaternion group $Q_8$, and found that spin spacetime separates into two complementary spaces: a spin polarization spacetime of even parity states, and a spin coherence space, in the $S^3$ hypersphere, of odd parity coherent states. Under the quaternion group, spin is a boson of spin 1 in free flight and a fermion of spin $\frac{1}{2}$ when measured. It immediately follows that neutrinos are not needed to balance spin and conserve energy in beta decay. Additionally, we find the boson electrons emitted in beta decay are odd to parity, leading to parity conservation even though the observed beta distribution is asymmetrical.

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights in quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows to extract high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo which enables calculations on large finite systems. Finite-size scaling can then be used to determine physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

Microfiltration membranes derived from semi-crystalline polymers face various challenges when synthesized through the extrusion–casting technique, including the use of large quantities of polymer, long casting times, and the generation of substantial waste. This study focuses on synthesizing these membranes using spin-casting followed by stretch-induced pore formation. Recycled high-density polyethylene (HDPE) and virgin polyethylene powder, combined with a calcium carbonate filler, were used as the source materials for the membranes. The influence of the polymer-filler ratio with and without stretching on the morphology, tensile strength, and water flow rate was investigated. Optimal conditions were determined, emphasizing a balance between pore structure and mechanical integrity. The permeable membrane possessed a mean pore diameter of 500 nm, exhibited a tensile strength measuring 32 MPa, allowed water to flow at a rate of 19 ml/min, and had a water contact angle of 126°. These membranes effectively eliminated suspended particles from water, with their performance evaluated against that of commercially available membranes. This research outlines a synthesis route for microfiltration membranes tailored to semi-crystalline polymers and their plastic forms, utilizing the spin-casting technique.