Physics

Although the fundamental equations of motion for particles are time-reversal symmetric, meaning they theoretically allow processes to run backward, the second law of thermodynamics imposes a directionality by stating that entropy tends to increase over time. This creates an effective 'arrow of time' because processes that decrease entropy are practically impossible, resolving the Loschmidt paradox. The recent mathematical insights show how molecular motions in fluids contribute to this irreversibility, explaining why time cannot flow backward in practice.

Individual molecules exhibit stochastic and dissipative motions that, when aggregated, produce irreversible fluid behavior. These microscopic molecular motions break time-reversal symmetry at the macroscopic level, leading to entropy production and the observed unidirectional flow of time in fluids. This mathematical grounding links molecular dynamics directly to the fundamental nature of time's arrow.

Physics-Informed Neural Networks (PINNs) are neural networks that incorporate physical laws described by partial differential equations (PDEs) into their training process. They solve inverse PDE problems by minimizing a physics-informed loss function that measures how well the network's output satisfies the PDE and any initial or boundary conditions, even without labeled data. This allows PINNs to infer unknown parameters or fields in PDEs from observed data by embedding the governing physics directly into the learning process.

PI-DIONs extend the PINN framework by learning solution operators for inverse PDE problems without requiring large labeled datasets. They incorporate stability estimates from inverse problem theory into operator learning, enabling robust and accurate inference of unknown quantities from measurement data. This approach allows real-time inference at arbitrary resolutions and better generalization across the domain, overcoming limitations of supervised models that depend heavily on labeled data and may fail to capture underlying physics accurately.

A 'forbidden' particle transition refers to a process that is not allowed under certain selection rules or approximations in physics, such as the electric dipole approximation. However, these transitions can still occur at a much lower probability through higher-order effects like magnetic dipole or electric quadrupole interactions. Forbidden transitions typically have much longer lifetimes compared to allowed transitions and are important in understanding rare or unusual particle behaviors.

Certain particle decays or reactions are forbidden because they violate fundamental conservation laws, such as conservation of baryon number or strangeness. For example, a decay that changes the total baryon number is forbidden. These conservation laws govern which particle interactions can physically occur, and forbidden decays do not happen because they would break these fundamental symmetries.

Tensors are algebraic objects that describe multilinear relationships between sets of algebraic objects associated with a vector space. They include scalars and vectors as special cases and are used to represent complex physical phenomena, such as stress and electromagnetic fields. Tensors are defined by their transformation properties under changes of coordinates, which distinguishes them from vectors and scalars (Kolecki, 2002; Porat, 2014)[2][3].

Tensors are crucial in physics and engineering because they provide a concise framework for formulating and solving problems in mechanics, electrodynamics, and general relativity. They are used to describe stress, elasticity, electromagnetic fields, and other complex phenomena. Tensors allow for the representation of these phenomena in a way that is invariant under changes of coordinates, making them essential for modeling real-world systems (Levi-Civita & Ricci-Curbastro, 1900; Kolecki, 2002)[1][2].

The mystery involved five high-lying vibrational states of the magnesium dimer (Mg2) molecule that had eluded detection for 50 years. While the lowest fourteen vibrational states were discovered in the 1970s, experiments predicted a total of nineteen states. The missing five states were key to understanding how the magnesium atoms interact quantum mechanically, but they remained undetected until recent computational advances solved this enigma.

Understanding the complete vibrational spectrum of the magnesium dimer provides a fundamental probe into quantum mechanical interactions between atoms. This knowledge can enhance the study of ultracold physics and chemistry, which are crucial for developing quantum technologies. Additionally, it can improve models used in astrophysics to understand molecular behavior in space, potentially leading to innovative advancements and deeper insights into the universe.

The puzzle involved the relationship between the second and third laws of thermodynamics, specifically the Nernst heat theorem and the unattainability of absolute zero. Historically, Nernst argued that absolute zero is unreachable because otherwise a perfectly efficient engine could be built, violating the second law. Einstein countered that the Nernst theorem was a separate third law. Martín-Olalla resolved this by showing that the third law actually derives from the second law when considering a virtual engine concept, thus unifying the principles and correcting Einstein's interpretation.

The virtual engine is a theoretical construct used to formalize the second law of thermodynamics without violating it. Unlike a real engine, it does not consume heat or produce work. Martín-Olalla used this concept to demonstrate that entropy exchanges tend to zero as temperature approaches absolute zero, which supports Nernst's theorem and the unattainability of absolute zero as direct consequences of the second law. This approach clarifies the natural zero of temperature as a physical quantity rather than a subjective sensation or empirical parameter.