  There is a common view in thermodynamics that the behavior of a macroscopic
system can be described by only a few state variables. Although this is true
for many cases, it is unclear whether it is meaningful to ask how many state
variables are acceptable. This is indeed a problem when solids are investigated
within the framework of thermodynamics, which is scarcely discussed in
textbooks. The present study gives an answer to this question: the mean values
of all the atom positions of a given solid together with the internal energy
constitute a commensurate set of state variables (thermodynamic coordinates,
TCs). The argument begins with constructing consistent definitions of
equilibrium and TCs. TCs are created by the constraints which characterize the
system under consideration. The values of TCs are uniquely determined in
equilibrium and the mutual relationships between them constitute the
fundamental relation of equilibrium (FRE). Specific heat can be deduced from
the FRE. Therefore, the TCs of a solid must be to give a full expression of the
specific heat in the entire range of temperature, from which the above
conclusion is deduced. Contrary to the conventional view, an infinite number of
the atom positions and their microscopic characters do not conflict with the
principles of thermodynamics. The most important requirement for TCs to meet is
the uniqueness of their values in equilibrium against random motions of the
constituent particles. This conclusion is compatible with the principle of
information theory that the information needed to determine the probability
distribution of states is the expectation values of statistical variables. A
few working examples of TCs in solids are given.
