This is the context, from an English translation of Dostoyevsky's Crime and Punishment. The word "service" here means military service.
'Funny fellow!' pronounced the innkeeper. 'And why don't you work, why aren't you at your duty, if you are in the service?'
Now, I know that there's a phrase "on duty" which TFD defines as:
Engaged in or responsible for assigned work.
Also one of TFD's definitions for "duty" says:
c. Active military service: a tour of duty.
but military service is not a physical location but an abstract concept, therefore I'm confused about the usage of the preposition "at."
TFD lists one of the synonyms for "duty" as "job".
Does "why aren't you at your duty" mean "why aren't you at your job" (the physical job location)? or perhaps it's the same as "why aren't you on your duty?"
Can you use the preposition "at" when speaking about an abstract concept?