# How is it possible that entropy of the universe has increased since big bang but temperature of the universe has decreased?

How is it possible that entropy of the universe has increased since the big bang, but the temperature of the universe has decreased?

I know that the increasing temperature of the system tends to increase in the entropy of the system thing tends to go higher entropic states.

Here System = Universe.

## 2 Answers

The universe is expanding, so its volume is constantly increasing, stretching out radiation wavelength and cooling down and decreasing the density of matter, which increases entropy, also entropy always increases in an isolated system. Entropy increasing/decreasing with temperature is only valid when kept in the same volume.

Maybe this wikipedia definitions will help:

In statistical mechanics, entropy is an extensive property of a thermodynamic system. It is closely related to the number Ω of microscopic configurations (known as microstates) that are consistent with the macroscopic quantities that characterize the system (such as its volume, pressure and temperature). Entropy expresses the number $$Ω$$ of different configurations that a system defined by macroscopic variables could assume. Under the assumption that each microstate is equally probable, the entropy $$S$$ is the natural logarithm of the number of microstates, multiplied by the Boltzmann constant $$k_B$$. Formally (assuming equiprobable microstates),

$$S=k_BlnΩ$$

In an expanding universe, the number of microstates is continually growing : in the beginning ( lets skip the quantum mechanical inflation time and count entropy after that) the continuous particle exchanges in the quark gluon plasma, the continuous radiation from charged particles inevitably lead to a large increase with time of the number of microstates. There is black body radiation continuously from all masses , after all even now (which is one way of looking at starlight).