| Definition -
An adverbial clause that
(1) contains its own subject,
(2) has a non-finite verb or no verb at all,
(3) is separated from the rest of the sentence by a comma or commas, and
(4) is not introduced by a subordinator (e.g. because).
(1) The dinner having been prepared, I went to store.
(2) The building being empty once more, I waxed prolific.
Oxford English Dictionary - The term's first citation is from 1889:
"The notions usually expressed by an absolute clause in Latin are habitually denoted otherwise in Anglo-Saxon. [Ibid.] The absolute construction is not an organic idiom of the Anglo-Saxon language."
(M. Callaway Absol. Pple. in Anglo-Saxon vii. 51)
Quotation - "Absolute Clauses are clauses in which the Predicate is formed with a Participle instead of a Finite Verb, and which are equivalent in meaning to Adverb Clauses of Time, Reason, Condition, or Concession, or to an Adverbial Phrase expressing Attendant Circumstance."
(Source: C. T. Onions, Advanced English Syntax)