Yeah, where is the definition $ \mathbf{P=\frac{E}{V}}$ from? It most definitely does not hold for all systems.

There are systems for which $ \mathbf{P}=\frac{2E}{3V}$ and systems for which $ \mathbf{P=\frac{E}{3V}}$ and, generalizing, systems for which $ \mathbf{P=\frac{sE}{3V}}$ where the relation between energy and momentum is $E\propto p^{s}$ (independent of whether boson or fermions are in discussion).

So yes, they are closely related but most definitely aren't one and the same thing.

Yeah, where is the definition $ P=\frac{E}{V}$ from? It most definitely does not hold for all systems.

There are systems for which $ P=\frac{2E}{3V}$ (example: ideal classical gas) and systems for which $ P=\frac{E}{3V}$ (example: photon gas) and, generalizing these cases, systems for which $ P=\frac{sE}{3V}$ where the relation between energy and momentum is $E\propto p^{s}$ (independent of whether boson or fermions are in discussion).

So yes, they are closely related but they most definitely aren't one and the same thing.

Yeah, where is the definition $ \mathbf{P=\frac{E}{V}}$ from? It most definitely does not hold for all systems.

There are systems for which $ \mathbf{P}=\frac{2E}{3V}$ and systems for which $ \mathbf{P=\frac{E}{3V}}$ and systems for which $ \mathbf{P=\frac{sE}{3V}}$ where the relation between energy and momentum is $E\propto p^{s}$ (independent of whether boson or fermions are in discussion).

So yes, they are closely related but most definitely aren't one and the same thing.

Yeah, where is the definition $ \mathbf{P=\frac{E}{V}}$ from? It most definitely does not hold for all systems.

There are systems for which $ \mathbf{P}=\frac{2E}{3V}$ and systems for which $ \mathbf{P=\frac{E}{3V}}$ and, generalizing, systems for which $ \mathbf{P=\frac{sE}{3V}}$ where the relation between energy and momentum is $E\propto p^{s}$ (independent of whether boson or fermions are in discussion).

So yes, they are closely related but most definitely aren't one and the same thing.