Its arguments are exclusively extensive variables of state.
2.
The extensive variables of the system are fundamental.
3.
Such splitting and recomposition is in accord with the above defined additivity of extensive variables.
4.
The corresponding extensive variable can be the number of moles of the component substance in the system.
5.
Legendre transformation is necessary because mere substitutive replacement of extensive variables by intensive variables does not lead to thermodynamic potentials.
6.
The thermodynamic force is always an intensive variable and the displacement is always an extensive variable, yielding an extensive energy transfer.
7.
Once we know the entropy as a function of the extensive variables of the system, we will be able to predict the final equilibrium state.
8.
But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values.
9.
If the assumption that the particles in an ideal gas are indistinguishable is not appropriately taken into account, the calculated entropy is not an extensive variable as it should be.
10.
The intensive ( force ) variable is the derivative of the internal energy with respect to the extensive ( displacement ) variable, while all other extensive variables are held constant.
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