Question about nuclear reation

Question

In Landau and Liftshitz Volume 5 page 318, it talks about nuclear reaction in high density, where proton reacts with electron and becomes neutron and neutrino:

$$A_z+e^- = A_{Z-1}+\nu$$

where $A_z$ is a nucleus of atomic weight $A$ and charge $Z$.

Then it says:

"The neutrinos are not retained by matter and leave the body; (1) such a process must lead to a steady cooling of the body. (2) Thus thermal equilibrium can be meaningfully considered in these conditions only if the temperature of the substance is taken as zero. (3) The chemical potential of the neutrinos will not then appear in the equation of the equilibrium."

(1), (2) and (3) seem to make sense to me but I feel I don't really understand. Can the experts give me more insights?

My questions are,

1) why removal of neutrinos will lead to cooling of the substance? Can this be endothermic instead?

2) And even it is cooling, why it is ok to discuss at T=0 if it never reaches equilibrium?

3) Why if a substance (neutrino) will be removed, we don't need to consider this in the equation of equilibrium.

Answer 1

1) Neutrinos carry energy. Allowing them to escape means that energy escapes the system, cooling it down.

2) When an object is at thermal equilibrium, it receives just as much energy from the environment as it emits. Because the probability of a neutrino interaction from the environment is so vanishingly low, this means that the object essentially receives zero energy from the environment. This means that the only way for the object to be in equilibrium with its environment is if it is also not emitting any energy, which only happens at zero temperature.

3) In a reaction at equilibrium, the forward and reverse rates of the reaction exactly balance, leading to a stable concentration of each reactant and product. But the reverse reaction that converts neutrinos into matter is so vanishingly improbable that its rate is effectively zero; hence, the neutrinos will never be at chemical equilibrium, and their contribution to equilibrium conditions can be neglected.