Entropy in thermodynamics is confusing

The second law of thermodynamics states that heat flows from hotter objects to colder ones, and that matter tends to become more disordered over time. This tendency is encapsulated in the concept of entropy. However, entropy can be a difficult concept to grasp.

One example of this complexity can be seen when considering Earth as a closed system under thermal equilibrium with its surrounding space. Despite the vast expanse of outer space, we don't observe gases escaping Earth into the vacuum, due to the planet's gravitational pull. This leads me to speculate that entropy might not be measured relative to an absolute reference point, say zero degree or vacuum, but rather as the potential energy stored in the surrounding environment, which is a local property.

Entropy could, therefore, be considered in terms of the inverse of the Gibbs free energy equation: S = (G-H)/T, where S represents entropy, G is Gibbs free energy, H is enthalpy, and T is temperature. 

This view strengthens the first law of thermodynamics that energy is conserved, even for entropic energy, i.e., merging 2nd law into the 1st. When G and H merge near absolute zero, entropy approaches zero, consistent with the third law of thermodynamics.

DOI: 10.13140/RG.2.2.27037.63206 

Kinetics equation in diluted solution is wrong

For two molecules in a dilute solution to react, they must first overcome the solvent barrier and collide with each other before any chemical reaction can occur. This process is known as diffusion, with a classic example being the Brownian motion of pollen particles on the surface of water.

As illustrated in the figure, the diffusion process differs significantly from the collision of gas molecules in a non-diluted gas reaction. In a neat gas, the time dependence of molecular collisions is linearly proportional to the separation distance because there are no molecules in between them, i.e., a direct flight; while in a dilute solution, it follows a square root dependence, i.e., traveling with many connections. The total traveling time is very different in these two cases with respect to the distances of the target and probe molecules, which are determined by their concentrations in the solution.

This difference means that the typical second-order reaction rate law, based on the concentrations of the reacting molecules, does not hold for reactions involving diffusion, which are all chemical reactions in practice. Just like most professors cannot afford a direct flight to conferences, predicting an average arriving time based on distances linearly doesn't work. Despite this, the second-order dependence is still often presented as a general rule in textbooks, suggesting that this concept may need to be revised.

https://doi.org/10.1063/5.0238119

Quantum mechanics is incomplete

One foundational mathematical model in quantum mechanics is the Schrödinger equation. This equation describes how quantum systems, such as an electron orbiting an atomic nucleus, evolve as wave-like patterns in space and time, essentially creating a "movie" of vibrating quantum waves. Encoding a movie in a short equation was a common practice back then. 

His core idea is analogous to the vibration of a guitar string: the frequency observed at a specific point in space over time corresponds to the spatial frequency (or curvature) of the wave at any fixed moment in time. In his first paper on quantum mechanics, Schrödinger introduced a thought experiment involving a particle in a box to illustrate this model (1926): "If, however, the molecule is situated in a “vessel”, then the latter must supply boundary conditions for the function g , or in other words, equation (41), on account of the introduction of further potential energies, will alter its form very abruptly at the walls of the vessel, and thus a discrete set of Ei-values will be selected as proper values."

The solution to the Schrödinger equation involves complex-valued wavefunctions, consisting of both real and imaginary components. However, textbook treatments often emphasize only the real part of the wavefunction (as shown on the left side of the figure), which can make it difficult to explain why certain spatial regions appear to have a value of zero, giving nodes on their modulus, where ideally zero should be a transient value.

The prevailing explanation for this simplification comes from the Copenhagen interpretation, which states that the modulus (or absolute value) of the wavefunction determines the probability of finding the particle in a given region of space. While this interpretation has become standard, it is also famously non-intuitive, so much so that it was strongly questioned by notable physicists such as Einstein, Schrödinger, and de Broglie. Einstein proposed the entanglement theory, Schrödinger proposed the thought experiment on cats in boxes, and de Broglie proposed the pilot wave theory, to challenge the Copenhagen interpretation.

My suggestion is why not add back the imaginary wave and make the wavefunction complex again, such that the probability or average momentum of the particle over space is uniform (right side of the figure). Adding the missing half of the wavefunction makes it complete. 

10.26434/chemrxiv-2022-xn4t8-v23 

An associated question is: what is light? I can say I truly don't know the answer, but these days it feels to me that light is nothing but particles, back to Newton's and Einstein's belief, rather than the commonly accepted idea of being both particle and wave.