I was reading this question and talking about it with my flatmate when a question came up. Ignoring the effects of losing or gaining mass due to cosmic dust, meteorites, and atmospheric losses as described here, has the Earth overall lost mass due to the entropy generated in the chemical reactions since the start of life?
What I'm thinking is that all of life uses resources from the Earth, whether it be plants extracting chemicals from the soil or digging up uranium for use in nuclear reactors. These materials then undergo chemical changes, thus increasing entropy. It could be argued that trash is buried so the mass change neutral but the items in the trash have been chemically altered at some point, therefore they technically weigh slightly less than their constituents.
Even trash that is burned "returns" to the Earth in the form of smoke in the atmosphere, right? But burning is a chemical reaction which again increases entropy. So if life had never developed on Earth and it was isolated from the rest of the cosmos, logically it should weigh more because less mass was converted to energy in reactions. Does that sound right?