On Posix, it is documented that setting PATH to the empty string is equivalent to not setting PATH at all, which is an exception to the rule that in a string like "/bin::/usr/bin" the empty string in the middle gets interpreted as ".".

PYTHONPATH does not have this exception: an empty PYTHONPATH is interpreted as equivalent to ".".

This difference is not documented.  This is a detail, but a possible source of confusion, so I'm reporting it here.

How to reproduce:

file x/x.py: "import z"
file z.py: "print(42)"

The following two lines behave differently (Bash syntax):

PYTHONPATH= python x/x.py
unset PYTHONPATH && python x/x.py

For comparison, if "./foo" is an executable, the following two lines behave identically (neither finds "./foo"):

PATH= foo
unset PATH && foo