Questions about the double ratchet mechanism in Signal
An eavesdropper who briefly compromises one of the parties might learn the value of a current ratchet private key, but that private key will eventually be replaced with an uncompromised one. At that point, the Diffie-Hellman calculation between ratchet key pairs will define a DH output unknown to the attacker.


This brief compromise is a of the current ratchet private key, one of the keys which I believe are called 'medium-term' in the DH paper (or at least in this security analysis. This means that the compromised key is only able to decrypt the current message, or messages in the current session before the key is ratcheted forward. 

This is part of how signal provides both forward and future secrecy - the medium-term key for this session cannot decrypt any past messages, and as soon as the key is refreshed it won't be able to decrypt any future messages.


  If the user is compromised at time T during a communication, isn't it true that the device is considered compromised for all time > T? If so why is the above assertion in the paper good? 


This would be true if the long-term key was compromised as well as a medium term key, but in fact signal protocol also uses ephemeral public keys which are stored on the signal servers and also replaced every so often, meaning that theoretically even if a session's medium term and ephemeral private keys were compromised, future sessions would still be secure.

didn't go into too much detail but can dig into the paper and explain a bit more if you would like. Does this help?