Both the Black-Scholes PDE and the Mass/Material Balance PDE have similar mathematical form of the PDE which is evident from the fact that on change of variables from Black-Scholes PDE we derive the heat equation (a specific form of Mass Balance PDE) in order to find analytical solution to the Black-Scholes PDE.
I feel there should be some physical similarity between the two phenomenon which control these two analogous PDE's (i.e. Black-Scholes and Mass/Material Balance). My question is whether you can relate these two phenomena physically through their respective PDE's? I hope my question is clear, if not please let me know. Thanks.