[Fzang]

To have a spontaneous adiabatic process, does the entropy have to be positive/negative? Or is entropy alone not a deciding factor?

If yes/no to above, then why? I know that S(system) + S(surroundings) equal/above 0, but how does this relate to an adiabatic system?

[novikovs]

Well, I was googling a similar question and have found only yours with no answers …

I got this question because some Russian textbooks on physical chemistry state the Second Law in a bit different way than the English ones, in terms of entropy (with my comments in brackets):

An English book (Atkins, 8-th ed., p.78): “The entropy of an isolated system increases in the course of a spontaneous change”.

A Russian book (Gerasimov et al. 1964, p. 90): “The entropy of an adiabatic system (i.e. where an adiabatic process occurs) increases in irreversible processes (i.e. spontaneous processes)”.

Note the difference: according to the Russian version, the system need not to be isolated to consider its entropy change as an indicator of spontaneity - i.e. as the total entropy change; the system just need to be thermally insulated (to make the process adiabatic) so that heat will not go out or in but work can go out or in!
In other words, if an adiabatic process occurs in a system then the system can do work (i.e. be not isolated) and we still can consider its entropy change as the total entropy change.

A simple explanation here is that work does not change the entropy of the surroundings (or anything), so the entropy change of the system in an adiabatic process becomes the total entropy change if we want to consider the system and the surroundings as an isolated system.

So, if you believe Russian textbooks, the answer to your question will be just the statement of the Second Law in the Russian version.
It is strange but I have not found yet any similar statement in English...

[novikovs]

Arguing with myself, I must admit that the above phrase “work does not change the entropy of the surroundings (or anything)” is not correct because we can use this work to produce heat in the surroundings which will change its entropy.
I believe it is correct to say that the work done by the system on the surroundings does not change the entropy of this system and, unless this work is converted to heat in the surroundings, the entropy change of that adiabatic system will be the total entropy change – i.e. of system plus surroundings.
Well, it makes me think that the phrase from the Russian book I cited above is not really a statement for the Second Law.