Other academic field distinctions like math vs maths
The abbreviations "stat mech" and "stat mechs" for statistical mechanics are both found by Google. I haven't analyzed the results to see whether there is a U.S./U.K. difference, although both abbreviations can be found associated with both countries.
'Mathematics' is defined thus at Collins:
mathematics n
(Mathematics) (functioning as singular) a group of related sciences, including algebra, geometry, and calculus, concerned with the study of number, quantity, shape, and space and their interrelationships by using a specialized notation
(Mathematics) (functioning as singular or plural) mathematical operations and processes involved in the solution of a problem or study of some scientific field
RHK Webster's concurs.
There is no rule as to how abbreviations must be formed. For instance, 'Buckinghamshire' is usually shortened to 'Bucks'. In the US, the word 'mathematics' is usually shortened to 'math', whereas in the UK, it is usually shortened to 'maths'.
When it comes to 'statistics', there is a common count noun usage. Thus the mean is one statistic; standard deviation and variance are two other statistics. For the field, singular concord is used though the noun derives from the plural. I believe that people in the US and Canada mostly use 'stat' as the abbreviation, whereas in the UK it's 'stats'. I seem to remember that most Canadians use 'maths', however!
Consider "sport" vs. "sports" when making reference to the general activity.
There's an AmE/BrE difference between saying "He is good at sports" and "He is good at sport," or saying "He studies sports" and "He studies sport."
The former is shared in both AmE and BrE, whereas the latter is a lot more typical of BrE.