Second, I used to believe that there is no real boundary, but upon reflection realized that this is completely wrong. Not only is there a physical boundary, this boundary is essential because living systems must distinguish between themselves and the things in the universe that are potentially available to be used as resources to stay alive.
In fact, there are multiple physical boundaries in living systems at various levels of hierarchy, starting with the defining characteristic of most life on earth (by number of species, not total number of individuals or percentage of biomass) which is that it is eukaryotic and so has a boundary around the cell nucleus. Then there are cell walls, the segregation of cells into organs, and finally, your skin, which delineates a physical boundary around you. Yes, some of these boundaries are a little bit fuzzy. But that doesn't mean they don't exist.