How can rubbing alcohol or witch hazel help a sore muscle?

Hmm well I always read the backs of bottles when I’m in the bathroom with time on my hands and this question has bothered me since I was about 12 but I can’t find an answer with google. The alcohol and witch hazel say “use on sprains, bruises, sore muscles.” How does putting something like that on your skin do anything for problems under the skin?

Also, is the answer to this question common knowledge?