  In glass physics, order parameters have long been used in the thermodynamic
description of glasses, but the nature is not yet clear. The difficulty is how
to find order in disordered systems. The usual treatment of glass as an
exceptional case causes serious internal inconsistencies in thermodynamics. The
issue turns out to be ascribed to a fundamental problem of defining state
variables in thermodynamics. This study provides a coherent understanding of
the nature of order parameters for glasses and crystals, starting from the
fundamental issue of defining state variables in thermodynamics. The state
variable is defined as the time-averaged value of a dynamical variable under
the constraint conditions, provided that the time average converges to a unique
value. This property is called time invariance. It gives the same value at any
time it is measured once an equilibrium is established. From this definition,
it is deduced that the state variables of a solid are the time-averaged
positions of all atoms constituting the solid, regardless of periodicity. The
general properties of order parameters are fully compatible with the time
invariance of state variables. For glass, equilibrium positions are state
variables and order parameters too. Because equilibrium positions are order
parameters, any property determined by equilibrium positions can also be an
order parameter. This explains why many quantities can be used for order
parameters. Symmetry introduces redundancy among the averaged positions of the
atoms, reducing the number of independent state variables. The often-claimed
association of order to periodicity lacks generality as explained by abundant
examples of well-ordered material, such as DNA. Order in thermodynamics means
the time invariance.
