Should I send a thank you note to the reply of a potential PhD adviser? I am considering applying for PhD degree. Regarding this I contact many professors to see if they are accepting new students or if I am a good fit for their research group. The responses will be different. 

For some of them, if lucky, they tell you the instruction, e.g. send your CV, contact me for the research you have done etc. However, you may receive a general email which most of the times means he/she is not interested in your CV. They write a general description of the application process or maybe a rejection to your request.

What should I reply back to these kind of responses from professors?
I would say, write a very brief e-mail in response saying something along the lines of "Understood, thank you very much." It's probably unnecessary, but it takes fifteen seconds to write and five to read and delete.

In particular -- a thank you note has essentially no possibility of annoying the professor, at least if it is not also accompanied by some sort of request. I would say -- if you are contemplating writing a brief thank you, then you may as well do so.