Statistical physics : Irreversibility

[dontknow]

TL;DR Summary

The Entropy of an isolated always increases.

I was reading mehran kardar (books and lectures) it says the concept of irreversibility comes from an assumption (in which we increase the length scale by interaction disctance between two particles).
So My question is the concept of irreversibility is still valid in the case of 1 particle.

Let's take an example from Feynman 2nd volume; A hydrogen atom going from excited to ground state is more probable thing to happen than a de-excited electron get excited by a photon. His explanation is that for an excited state initially entropy is low because photon (in final state) is something that is wandering in different direction so there is an increase in entropy.

Coming back to question where does the explanation for irreversibility come for the case of 1 or few particle system.

 

[Dale]

A hydrogen atom always goes from excited to ground state, not the other way.

Hmm, that doesn't seem right. A hydrogen atom clearly can go from the ground state to the excited state too.

 

[atyy]

Coming back to question where does the explanation for irreversibility come for the case of 1 or few particle system.

The single atom is interacting with many other things that are not explicitly mentioned, such as the quantum state of the electromagnetic field surrounding the atom. The background electromagnetic field can provide a thermal bath for the atom.

The background section (first paragraph) of https://arxiv.org/abs/1510.04745v1 has some related references.

Chapter 3 of https://www.uibk.ac.at/th-physik/cqed/theses/bachelorthesis_kruckenhauser_andreas.pdf models spontaneous emission by coupling the atom to the background electromagnetic field.

 

[Lord Jestocost]

Summary:: The Entropy of an isolated always increases.
Coming back to question where does the explanation for irreversibility come for the case of 1 or few particle system.

Maybe, Feynman's reasoning can be easier understood when one conceptually explains “entropy” qualitatively in the following way:

The second law of thermodynamics says that energy of all kinds in our material world disperses or spreads out if it is not hindered from doing so. Entropy is the quantitative measure of that kind of spontaneous process: how much energy has ‘flowed’ from being localized to becoming more widely spread out (at a specific temperature). [Quotation marks by LJ]

Frank L. Lambert in “Entropy Is Simple — If We Avoid The Briar Patches!” (http://entropysimple.oxy.edu/content.htm#increase)

Thermodynamic processes entail spatial redistributions of internal energies, namely, the spatial spreading of energy. Thermal equilibrium is reached when energy has spread maximally; i.e., energy is distributed equitably and entropy is maximized.

Harvey S. Leff in “Removing the Mystery of Entropy and Thermodynamics – Part I” (Phys. Teach. 50, 28 (2012))

Feynman (in “Feynman lectures Vol. III”, Chapter 7.1) puts it in the following way:

Why does an atom radiate light? The answer has to do with entropy. When the energy is in the electromagnetic field, there are so many different ways it can be—so many different places where it can wander—that if we look for the equilibrium condition, we find that in the most probable situation the field is excited with a photon, and the atom is de-excited. It takes a very long time for the photon to come back and find that it can knock the atom back up again.

 

[anorlunda]

The whole subject of thermodynamics including the 2nd law, is based on statistical mechanics. You can't apply statistics to 1 or 2 particles. You can't define temperature or entropy for 1 or 2 particles.

For example, what is the temperature of a free electron? There is no answer, the concept of temperature does not apply to a single particle.

Indeed, at the atomic level where we track every particle, almost all (not all but almost all) are time reversible.

 

[vanhees71]

Hmm, that doesn't seem right. A hydrogen atom clearly can go from the ground state to the excited state too.

Indeed, and in equilibrium the rate of excitation is the same as that of the relaxation.

The H theorem (increase of entropy) follows from the unitarity of the S matrix and Boltzmann's "molecular-chaos assumption" to truncate the BBGKY hierarchy in the usual way by approximating the two-particle phase-space distribution function with the product of the corresponding single-particle distribution functions.

 

[rentier]

You can't define temperature or entropy for 1 or 2 particles.
...
There is no answer, the concept of temperature does not apply to a single particle.

For sure?
What about the average over time (ergodicity)?
In statistical mechanics temperature is an average kinetic energy.

 

[DrClaude]

For sure?
What about the average over time (ergodicity)?
In statistical mechanics temperature is an average kinetic energy.

Then you don't have a single particle, but an individual particle interacting with a reservoir.

 

[vanhees71]

For sure?
What about the average over time (ergodicity)?
In statistical mechanics temperature is an average kinetic energy.

Sure, you can define temperature for a single particle coupled to a heat bath. Look for Fokker-Planck and/or Langevin equation.

 

[rentier]

Indeed, at the atomic level where we track every particle, almost all (not all but almost all) are time reversible.

What is an example for _not_ reversible? (in statistical mechanics, not quants)