Journal to myself as I read Volume III of the Feynman Lectures in Physics (as a commitment mechanism).
Chapter 1
Feynman begins by noting that physics at very small scales is nothing like everyday experience, which means we will have to rely on an abstract approach. He then presents the double-slit experiment, first imagining bullets passing through the screen, then water waves, and finally the quantum behavior of electrons. I found myself checking I could still derive the law of cosines. He emphasizes that all things, in fact, behave in the quantum way electrons do, although for large objects it is very hard to tell. I enjoyed the “practicality” of his descriptions, for example describing the electron gun as a heated tungsten wire in a box with a small hole in it. He concludes by introducing the uncertainty principle.
Chapter 2
This chapter is largely devoted to example realizations of the uncertainty principle. For example, if particles pass through a slit of width L, we then know their position with an uncertainty of order L. However, the slit will give rise to diffraction, which reflects uncertainty regarding the particle’s momentum. If we narrow the slit, the diffraction pattern gets wider. The uncertainty principle is also used for a heuristic estimate for the size of a hydrogen atom. We write an energy for the electron E = p^2/2m—q^2/r, where m and q are the mass and charge of the electron. If the momentum is of the order given by the uncertainty relation, p = h / r, we can replace it in E and find the distance r that minimizes the energy. This yields a figure on the order of angstroms, which is the correct scale for atoms. The chapter concludes with a brief philosophical discussion regarding what is real and indeterminacy in quantum and classical mechanics.
In the case of epigenetic memory based on freely-diffusing factors, the alternative “stable” states can probably be thought of as long-lived metastable states in “real” stochastic system, which become stable fixed points in the limit as the number of particles N goes to infinity. In models, the switching time often grows exponentially with the number of particles. You may enjoy https://arxiv.org/abs/q-bio/0410003 or https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.208101.
For memory based on chemical modifications embedded along the genome, like DNA methylation, there isn’t really a “large N” limit to take, and in my view things are less settled. You may enjoy https://pubmed.ncbi.nlm.nih.gov/17512413/ or (shameless plug) https://www.science.org/doi/10.1126/science.adg3053