Physical meaning of $SdT$

Question

Consider a thermodynamic classical closed system. Due to the First and Second laws of thermodynamics, we know that $dU=\delta Q-\delta W=TdS-PdV$, and we could assign to $\delta Q=TdS$ the meaning of exchanged heat.

But what physical meaning could we assign to $SdT$ appearing, e.g., in the expression for a reversible Helmholtz free energy variation, $dA=-SdT-PdV$?

Answer 1

Simple & short answer:

Consider the constant V case (say, you have a fixed size container of a gas): The $dA$ then is given by $$dA = -SdT$$ Thus $SdT$ : For a fixed volume container, how much free energy will decrease by increasing the temparature of the system.