  Entropy and order parameter are two key concepts in phase transition theory.
This paper proposes an unified method to both find order parameter and estimate
entropy automatically with unsupervised learning. The contributions of this
paper are threefold: First, it is shown that the cross-entropy loss of an
optimum autoencoder could be used to estimate the physical entropy, which also
explains why the critical temperature can be identified by the inflection point
of the reconstruction loss. Second, a series of interpretable autoencoders are
proposed which reproduce the ferromagnetic/antiferromagnetic (F/AF) order
parameter in special cases. They provide us an intuitive prototype to
understand the connection between unsupervised learning and phase transition
theory. Third, we analyze spin glass phase with our method, the results suggest
a "distributed" order parameter to describe spin-glass ground state, which is a
natural generalization of F/AF order parameter with respect to the autoencoder.
