# Functions of state and definition of equilibrium

Consider this - A function of state is any physical quantity that has a well-defined value for each equilibrium state of the system. (Blundell and Blundell - Thermal Physics)

My question is - Are equilibrium states not defined by the function of state variables themselves?

That is,function(s) of state defines a equilibrium state and function(s) of state are themselves characterised by having a unique/well-defined value at an equilibrium point.

Is this not a circularity?

Now if we look at the state variable like internal heat, entropy, etc we will find that they are depending on these thermodynamic terms which i mentioned above. For example take the example of internal heat. The first law of thermodynamic says that the cyclic integral of heat is equal to the cyclic integral of the work done from which on further solving we get the expression of $dU=\delta Q-\delta W$. so we can see that $dU$ is depending on the temperature, pressure, etc.