"No trace" conceptual origins and term

There is a quote by Shunryu Suzuki which says: > When you do something, you should do it with your whole body and mind; you should be concentrated on what you do. You should do it completely, like a good bonfire. You should not be a smoky fire. You should burn yourself completely. If you do not burn yourself completely, a trace of yourself will be left in what you do. I think I've read this elsewhere described in terms of a snowflake in a fire, and everything turned to ash. Is there an original source(s) of this concept, and if so, is there a succinct name for it in Chinese or Japanese Zen?