Basic problem in equilibrium thermodynamics

[kini.Amith]

I was reading Thermodynamics by Herbert Callen. In the first chapter he makes the following statement.
'The basic problem of thermodynamics is the determination of the equilibrium state that eventually results after the removal of internal constraints in closed composite system.'
Then he postulates
'There exists a function (called the entropy) of the extensive parameters of any composite system, defined for all equilibrium states and having the following property. The values assumed by the extensive parameters in the absence of an internal constraint are those that maximise the entropy over the manifold of constrained equilibrium states.'
In the first statement, what does he mean when he says 'the basic problem'. Does he mean that every problem in (equilibrium) thermodynamics can be reduced to the above problem?
If not, why is this problem so important as to postulate entropy on its basis?

 

[Useful nucleus]

Just keep reading this excellent text and you will figure out what the author means. He tends to recap every few sections. In particular cover chapter 2 and 3.

 

[Othin]

That's precisely what he means. As the postulate states, the entropy is only defined for equilibrium states, so that this approach can only study equilibrium states (If you think about it, even the definition of Temperature will lose it's meaning out equilibrium, since its definition is linked to the entropy function). The first postulate says that this state will always exist, making the theory consistent. Thus you can reduce every problem in the theory's range of applicability to the determination of the equilibrium states, which contain all the information you need. It's just like the basic problem of mechanics : to know the position and velocity in every instant t. If there is a function that contains this information, say, the Lagrangian, every problem in mechanics will be solvable in principle.