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The paper examines and critiques the expression of entropy as the logarithm of the number of quantum states of a physical system. Boltzmann method of expressing entropy as the logarithm of the number of states of a gas with a given total energy is analyzed. We demonstrate that entropy is the product of subquantum processes and show that entropy is expressed as the ratio of the logarithm of the maximum number of realizations, over the observation period, of a macroscopic system's states with a given total energy, to the number of occurrences of its quantum states over this time.
Twisted bilayer graphene (TBG) near the magic twist angle of $\sim1.1^{o}$ exhibits a rich phase diagram. However, the interplay between different phases and their dependence on twist angle is still elusive. Here, we explore the stability of various TBG phases and demonstrate that superconductivity near filling of two electrons per moiré unit cell alongside Fermi surface reconstructions, as well as entropy-driven high-temperature phase transitions and linear-in-T resistance occur over a range of twist angles which extends far beyond those exhibiting correlated insulating phases. In the vicinity of the magic angle, we also find a metallic phase that displays a hysteretic anomalous Hall effect and incipient Chern insulating behaviour. Such a metallic phase can be rationalized in terms of the interplay between interaction-driven deformations of TBG bands leading to Berry curvature redistribution and Fermi surface reconstruction. Our results provide an extensive perspective on the hierarchy of correlated phases in TBG as classified by their robustness against deviations from the magic angle or, equivalently, their electronic interaction requirements.
In the presence of a large perpendicular electric field, Bernal-stacked bilayer graphene (BLG) features several broken-symmetry metallic phases as well as magnetic-field-induced superconductivity. The superconducting state is quite fragile, however, appearing only in a narrow window of density and with a maximum critical temperature $T_c\approx30$~mK. Here, we show that placing monolayer tungsten diselenide (WSe$_{2}$) on BLG promotes Cooper pairing to an extraordinary degree: superconductivity appears at zero magnetic field, exhibits an order of magnitude enhancement in $T_c$, and occurs over a density range that is wider by a factor of eight. By mapping quantum oscillations in BLG-WSe$_2$ as a function of electric field and doping, we establish that superconductivity emerges throughout a region whose normal state is polarized, with two out of four spin-valley flavours predominantly populated. In-plane magnetic field measurements further reveal a striking dependence of the critical field on doping, with the Chandrasekhar-Clogston (Pauli) limit roughly obeyed on one end of the superconducting dome yet sharply violated on the other. Moreover, the superconductivity arises only for pe
There's a separate $1,750 rebate for used EVs, but both rebates have a price cap
Astronomers have uncovered 31 of the oldest known quasars, including the two earliest ever detected, shining from a time when the universe was only about 670 million years old。 Powered by supermassive black holes billions of times the Sun’s mass, these incredibly bright objects challenge scientists’ understanding of how such enormous black holes fo
A planet with one side permanently roasting and the other frozen in endless darkness might still have a chance of supporting life。 Researchers found that heat inside a tidally locked exoplanet could circulate in a stable, continuous loop, helping moderate temperatures in certain regions。 Their laboratory model suggests these worlds may be more hosp
NASA is ramping up its lunar ambitions by awarding nearly $600 million for four commercial Moon landings planned for late 2028。 Each mission will carry the same trio of science instruments to improve lunar navigation, study dangerous dust kicked up during landings, and map the Moon's radiation environment。 The agency also revealed plans for new rov
Scientists have identified new clues that could help astronomers spot one of the most famous hypothetical alien megastructures: a Dyson sphere。 The study finds that red dwarfs and white dwarfs are the most promising stars to examine, since advanced civilizations could potentially build energy-harvesting swarms around them more easily。 These objects
It's unclear how the planet avoided its star's bloated red giant stage
More police and firefighters use drones to catch and deter illegal fireworks
Celebrating the United States' 250th anniversary, NASA released a stunning Hubble portrait of Messier 3, an ancient globular cluster with more than 500,000 stars。 The remarkable cluster is helping scientists unravel the Milky Way's past thanks to its rare stars and possible origins in a long ago cosmic merger
Dark matter may be far more complicated than scientists once believed。 A new study suggests it could consist of at least two different kinds of particles that slowly separate over time, with heavier particles sinking toward the centers of galaxies and lighter ones drifting outward。 This simple idea could explain several puzzling cosmic observations
Researchers have achieved a major milestone by creating a long-sought two-dimensional quantum material and confirming its unusual conducting edge states。 The ability to control these states through strain could make the material a promising platform for future room-temperature quantum electronics
Scientists have rewritten the story of gallium after discovering that its unusual atomic bonds re-form at high temperatures, contradicting decades of accepted theory。 The finding changes how researchers explain why the metal melts so easily and behaves unlike almost any other metal。 Beyond solving a long-standing scientific mystery, the work could
Physicists from Heinrich Heine University Düsseldorf (HHU) have examined a fundamental property of quantum mechanics in collaboration with the German Aerospace Center (DLR)。 In the scientific journal Physical Review Letters, they show that this theory does not necessarily need to be formulated with imaginary numbers – real numbers can in fact also