The mathematical structure of thermodynamics

Thermodynamics is unique among physical and chemical descriptions of our surroundings in that it does not rely on a detailed knowledge of any interior structure of the systems to which it pertains but rather treats such systems as “black boxes” whose equilibrium states are determined by the surroundings with which they can coexist and which can be described by a few parameters. This feature assures that the theory holds true when the system is a collection of molecules, or a beaker of water, or a black hole. Einstein expressed this feature of thermodynamic theory in his classic quote: "Thermodynamics is the only physical theory of universal content which, within the framework of the applicability of its basic concepts, I am convinced will never be overthrown." — Albert Einstein Foremost among these basic concepts is the notion of equilibrium, the situation where the state of the system does not vary noticeably in time. The “noticeably” in the previous sentence has two complications. The first is that if this system were to be cut off from its surroundings the state would remain the same. This distinguishes equilibria from steady states. The second is the fact that the notion of equilibrium is associated with a particular time scale. Over larger periods of time, any system will eventually evolve until the final dead state of Fe is reached through nuclear transformations.