In this talk I will review the informational approach to thermodynamics, and how its laws can be derived from the postulates of quantum mechanics. I will focus on the third law of thermodynamics, formulated as the unattainability principle. This states the impossibility of cooling a system down to absolute zero in finite time, or with finitely-many resources. I will present a proof of the unattainability principle that applies to arbitrary (cooling) processes and provides a quantitative relationship between the duration of the process and the achieved final temperature. This result concludes a longstanding debate that goes back to Nernst and Einstein.