What is the meaning of the term more fundamental in this context?
The reason thermodynamics might be considered more fundamental is that it accounts for the observation that the actual system and its surroundings cannot both be restored to the initial conditions via a reversible process.
The reason Newtonian physics might be considered more fundamental is because it gives us the foundational theoretical concepts for system analysis and the comprehension of an ideal reversible process.
Reversible and Irreversible Processes
An irreversible process is what we encounter in reality almost all the time. The system and its environment cannot be restored to their original states at the same time. Because this is what happens in nature, it is also called a natural process. The sign of an irreversible process comes from the finite gradient between the states occurring in the actual process. For example, when heat flows from one object to another, there is a finite temperature difference (gradient) between the two objects. More importantly, at any given moment of the process, the system most likely is not at equilibrium or in a well-defined state. This phenomenon is called irreversibility.
I removed prior references and comments.