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The analytical solution of a free convection problem is particularly simple thanks to the introduction of a variable $x$ which describes the features of the phenomenon independently of the boundary conditions. The thermodynamical meaning of this variable is examined and the hypothesis is advanced that it generally represents the intensive conjugate of the internal energy and that the new couple obeys a general rule of symmetry similar to the other couples of coniugate variables such as $p-V$ and $S-T$. By assuming this model, 6 new thermodynamical potentials are written which are coincident with the 3 classical ones when the system is close to equilibrium. The 12 Maxwell's relationships reduce contemporarily to 4. The new description includes the Prigogine’s principle and may be applied to systems far from equilibrium. In particular, the time derivative of $x$ is aiways positive, providing a general picture of non-equilibrium which appears promising.

The analytical solution of a free convection problem is particularly simple thanks to the introduction of a variable $x$ which describes the features of the phenomenon independently of the boundary conditions. The thermodynamical meaning of this variable is examined and the hypothesis is advanced that it generally represents the intensive conjugate of the internal energy and that the new couple obeys a general rule of symmetry similar to the other couples of coniugate variables such as $p-V$ and $S-T$. By assuming this model, 6 new thermodynamical potentials are written which are coincident with the 3 classical ones when the system is close to equilibrium. The 12 Maxwell's relationships reduce contemporarily to 4. The new description includes the Prigogine’s principle and may be applied to systems far from equilibrium. In particular, the time derivative of $x$ is aiways positive, providing a general picture of non-equilibrium which appears promising.