Entropy and the $2^{nd}$ law of thermodynamics

I have just been introduced to the word "entropy" and as it is my understanding that it is a measure of the randomness and chaos of particles in as system.

My textbook list the 2nd law of thermodynamics in various forms one of them "The entropy of the universe can never decrease", but somewhere I read that the universe has been cooling ever since the big bang.

Should a system that is cooling not become less chaotic and random since there is less energy available for motion, vibration ect?

• The net entropy of the Universe is increasing. – Jiminion Feb 19 '15 at 19:21
• this seems to be counter-intuitive – Gobabis Feb 19 '15 at 19:25
• The cooling is due to adiabatic expansion (well at least the microwave background radiation part), as the universe is expanding, however adiabatic processes don't change the entropy (they are reversible, as they don't need any heat exchange). A very similar situation happens when a piston is compressed or depressed without heat exchange - this is a reversible process. – kristjan Feb 19 '15 at 20:02

it is my understanding that it is a measure of the randomness and chaos of particles in as system

There are many different kinds of entropy. "Measure of chaos" is very inaccurate characterization of all of them.

Second law of thermodynamics has consequences for changes in macroscopic bodies that can attain thermodynamic equilibrium state and thus be ascribed thermodynamic entropy - this is meaningful only for systems in thermodynamic equilibrium.

Thermodynamic equilibrium of body is a situation where macroscopic observations detect no macroscopic motions, no changes, no transfer of energy. Moreover, to apply thermodynamic theory to the system, its equilibrium state must be accessible to the system given external constraints. For gas, this means it has to be in a closed container, otherwise it will spread everywhere.

Universe is hardly such a system, for we know of no constraints to its volume or energy ; and thus there are no thermodynamic state variables entropy could be function of.

Universe has never been experimentally probed in such a way as air or steam in heat engines. To claim it is in thermodynamic equilibrium and can be ascribed thermodynamic entropy is unfounded. It is also meaningless to claim the whole universe obeys 2nd law of thermodynamics, when nobody has ever observed heat transfer between the universe and the reservoir and define temperature of the universe. Using 2nd law in such grand scenarios is a patently unfounded extrapolation of our experience with systems of size comparable to humans. In the whole universe, there is gravity and other things mostly ignored in all experiments on which thermodynamic theory was founded.

• " It is also meaningless to claim the whole universe obeys 2nd law of thermodynamics, when nobody has ever observed heat transfer between the universe and the reservoir" that really makes sense – Gobabis Feb 19 '15 at 19:44