Actually, walking through an unlocked door without authorization *is* B&E, at least in Massachusetts. Pushing open the door constitues the "breaking" element of the crime. If your intent is to commit a further crime, such as the taking of property that doesn't belong to you, it then becomes burglary.
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Date: 2006-05-10 06:00 pm (UTC)http://dictionary.law.com/default2.asp?selected=98&bold=
"Failure to secure does not imply permission to access."