uni = Union[list, SameTest -> (Abs[#1 - #2] < 10^-4 &)]
Total[Range[4, 1, -1] E^(uni/t)]
eldo
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uni = Union[list, SameTest -> (Abs[#1 - #2] < 10^-4 &)]
Total[Range[4, 1, -1] E^(uni/t)]