I'm asking about equation $(11.50)$ in Peskin and Schroeder where they state that the effective action evaluated at the classical field is given by

$$\Gamma[\phi_c] = -(VT)\cdot V_{eff}(\phi_c).$$

They claim that the $\Gamma$ is, in thermodynamic terms, an extensive quantity. Where do they get this information from?

I'm asking about equation $(11.50)$ in Peskin and Schroeder where they state that the effective action evaluated at the classical field is given by

$$\tag{11.50}\Gamma[\phi_c] = -(VT)\cdot V_{eff}(\phi_c).$$

They claim that the $\Gamma$ is, in thermodynamic terms, an extensive quantity. Where do they get this information from?

Does is simply come from the fact that $$\tag{11.47}\Gamma[\phi_c] = -E[J]-\int d^4y\, J(y)\phi_c(y),$$ where $$E[J]\sim \log \int \mathcal{D}\phi \exp\bigg[\mathrm{i}\int\mathrm{d}^4x\,(\mathcal{L}+J\phi)\bigg].$$

Then I guess one could say that $\Gamma\propto\int d^4x=VT.$

I'm asking about equation $(11.50)$ in Peskin and Schroeder where they state that the effective action evaluated at the classical field is given by

$$\Gamma[\phi_c] = -(VT)\cdot V_{eff}(\phi_c).$$

They claim that similar to the $\Gamma$ is, in thermodynamic terms, an extensive quantity. Where do they get this information from?

I'm asking about equation $(11.50)$ in Peskin and Schroeder where they state that the effective action evaluated at the classical field is given by

$$\Gamma[\phi_c] = -(VT)\cdot V_{eff}(\phi_c).$$

They claim that the $\Gamma$ is, in thermodynamic terms, an extensive quantity. Where do they get this information from?