Correspondence of the Symmetry of Thermodynamic Properties of Matter with the Symmetry of Equations of State.

Thermodynamics contains rich symmetries. These symmetries are usually considered independent of the structure of matter or the thermodynamic state where matter is located and, thus, highly universal. As Callen stated, the connection between the symmetry of fundamental laws and the macroscopic properties of matter is not trivially evident. However, this view is now being challenged. Recently, with symmetry to the ideal gas equation of state (EOS), an ideal dense matter EOS has been proposed, which has been verified to be in good agreement with the thermodynamic properties of high-density substances. This indicates that there is a certain symmetry between the thermodynamic properties of substances in their high- and low-density limits. This paper focuses on the distinctive features and the significance of this symmetry. It is a new class of symmetry that is dependent on the thermodynamic state of matter and can be incorporated into the existing symmetrical theoretical system of thermodynamics. A potential path for developing the EOS theory arising from this symmetry is discussed. EOS at high densities could be developed by correcting or extrapolating the ideal dense matter EOS based on this symmetry, which might fundamentally solve the difficulty of constructing EOS at high densities.