In response to a question whether or not one can perform melakhah as usual on Yom Tov Sheni Shel Galuyoth, Rav Ami responds (Pesahim 52a):
be-yishuv asur, ba-midbar mutar
…in the city it is forbidden, but in a desolate and uninhabited place it is permitted.
His statement seems to be recorded as the halakhah and no one appears to argue with him.
Does he actually mean what he seems to mean, and is it le-maaseh? Are we to actually understand him being matir work on the second day of a holiday as long as it doesn't produce shinuyei mahloqoth (see there)? If so what is the significance of it for our understanding of the nature of Yom Tov Sheni Shel Galuyoth? Does this statement indicate that Yom Tov Sheni has no actual sanctity when we are sure of the calendrical dates?
Please cite your sources. Thanks.