How do state functions differ from heat and work in thermodynamics?

In thermodynamics, the fundamental difference between state functions and quantities like heat and work lies in their dependence on the system's path.

State Functions

A state function, such as internal energy, is a property whose value is determined solely by the current equilibrium state of the system, defined by parameters like temperature, pressure, and volume. Because these functions depend only on the initial and final states, any change ($\Delta U$) is independent of the process used to reach that state. Mathematically, the incremental change of a state function is an exact differential.1234

Heat and Work

In contrast, heat ($Q$) and work ($W$) are not state functions; they are path-dependent quantities. Their values depend on the specific process or "path" taken to transition between states. Consequently, it is not meaningful to speak of the "heat content" or "work content" of a system, only the energy transferred across its boundaries. Mathematically, their incremental changes are not exact differentials, meaning their values must be evaluated based on the specific path taken.12345