Physicalism: A physical duplicate of our world (i.e. a world in which all the same physical properties are instantiated at the same space-time locations) must necessarily also be a mental duplicate (i.e. all mental states instantiated in that world must be identical to the mental states instantiated in this one).
A physical duplicate is identical to the original in its distribution of physical properties. This leaves open the possibility that there are non-physical properties which could differ between the worlds. Of course, if you believe there are no independent non-physical properties, then the physical duplicate would in fact be identical to the original.
Physicalism: A physical duplicate of our world (i.e. a world in which all the same physical properties are instantiated at the same space-time locations) must necessarily also be a mental duplicate (i.e. all mental states instantiated in that world must be identical to the mental states instantiated in this one).
Anti-physicalism: The denial of physicalism.
In what sense is a duplicate distinct from an original in these definitions?
A physical duplicate is identical to the original in its distribution of physical properties. This leaves open the possibility that there are non-physical properties which could differ between the worlds. Of course, if you believe there are no independent non-physical properties, then the physical duplicate would in fact be identical to the original.
“Same space-time location” means “same relative distances and time intervals within each world”?
Yes, that is what it means.