Connection between entropy, chance and principle of least action

The Principle of Least Action serves as the foundation for Newton’s laws. It can be derived from the path integral formulation in quantum mechanics (QM). Path integrals, resembling expressions such as ∫e^ix

, bear a resemblance to the integrals in statistical mechanics, specifically those of the form ∫e^(-βH).

These integrals, ∫e^(-βH), find their origin in the concept of entropy (S), where S is defined as k ln⁡ω. Here, k represents the Boltzmann constant, and ω denotes the multiplicity of quantum states. Thus, the intricate connection between the Principle of Least Action, quantum mechanics, and statistical mechanics unveils a rich tapestry of mathematical relationships within the realm of physical laws.

And another interesting connection is that general relativity can be derived from statisticla mechanical considerations.

Fermi gas and black holes

Looks like hawking radiation and the fermi surface an event horizon

Why are electrons identical to another?

Quantum particles are fundamentally identical and indistinguishable because there exists a reference frame where both particles appear as just a single particle. There world lines can be connected in a reference frame.

Why words are defective

You cannot name every real number, it is impossible. So there are more things in the world than words.