# Kinetic equilibrum and chemical equilibrium

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1. Jul 2, 2015

### karlzr

All particle species are in equilibrium at early times of the universe. But I didn't find any book that makes the difference of kinetic and chemical equilibrium clear. I have some of my own opinions and I hope to get your comments:
(1) kinetic equilibrium means the distribution function obeys the Bose-Einstein or Fermi-Dirac distribution with a well-defined temperature. This concerns only one specific particle species. Then kinetic equilibrium can be reached as long as it scatters rapidly enough with any particle while keeping its particle number unchanged: $a + b \to a + b$.
(2) While chemical equilibrium involves at least two particle species that are connected by processes that change the particle number: $a + b \to c + d$ or $a \to b + c$.
So whether some particle species such as $t$ quark is in equilibrium depends only on the thermally averaged cross section related to that specific kind of equilibrium. Thermodynamic equilibrium means both kinds of equilibrium are satisfied. Same temperature applies only to thermodynamic equilibrium, right?
So when we say some particle freezes out at some point, we really mean it is out of chemical equilibrium with the rest of the universe but it may still be in kinetic equilibrium with itself and thus maintain a different temperature.
Thanks,

Last edited: Jul 2, 2015
2. Jul 2, 2015

### rootone

I think you are confusing particles with atoms.
Atoms must exist in order for any kind of chemistry to happen.
In the very early Universe there were no atoms, and only after it had cooled considerably, atoms appeared.
However nearly all atoms at that time were hydrogen or helium, and those do not chemically react.
Much more time then elapsed before stars formed and other elements were produced, and more time still until these heavier elements became dispersed into the intersellar medium.
Only at that stage could any chemical processes occur.

Last edited: Jul 2, 2015
3. Jul 2, 2015

### Staff: Mentor

Not necessarily. The term "chemistry" can refer to nuclear reactions that change particle numbers. (More often you see related usage such as the term "chemical potential" to describe terms appearing in the thermodynamic equations for systems containing multiple particle species.) Such reactions certainly exist and are relevant under the conditions the OP is describing, so even if you don't like the term "chemistry" to describe what the OP is describing, what he's describing certainly occurs.

4. Jul 2, 2015

### rootone

Thanks.
I did not know of the term 'chemistry' being used in that context.
(but now i do - )

5. Jul 2, 2015

### Staff: Mentor

Basically, yes. What causes the "freezing out" is the rates of all relevant reactions that interchange the particle species under consideration with other species, becoming low enough to be negligible.