A derivation of the third law of thermodynamics

In the first part of the talk I will present a derivation of the third law of thermodynamics, which shows the impossibility of cooling matter to absolute zero, and quantifies the resources that are necessary to achieve any given temperature. This result also implies the impossibility of exact information erasure and quantifies the necessary resources for erasing information up to any given error (based on arXiv:1412.3828). In the second part of the talk I will show that all the alternatives to the measurement postulates of quantum theory, including the Born Rule, are in correspondence with a class of representations of the unitary group.