# Probability of a fluctuation/entropy decrease

shimzz5
Suppose we have a gas in the room at some temperature which is room temperature or higher.

In some references the probability is given by -ΔS, which is indeed a tiny number and makes sense.

However, in other references the probability is given by the Boltzmann factor plus the number of microstates -M/T + S, where T is the temparature of the gas and S the entropy of the fluctuated object. How to resolve this contradiction (between the microcanonical and canonical ensemble)? Shouldn't the entropy factor cancel the -M/T factor for ordinary temperatures? It seems that in the second equation (which corresponds to the free energy) the fluctuations are probable even now because the temperature is pretty high? Why don't we observe random fluctuations into low entropy states according to the second formula?

Sorry for my bad english, thanks.

## Answers and Replies

Mentor
2021 Award
In some references the probability is given by ...

However, in other references the probability is given by
Could you provide a link to these references? The context may help.

shimzz5
• Dale