  This is the first of a series of three articles that treats fracture
localization as a critical phenomenon. This first article establishes a
statistical mechanics based on ensemble averages when fluctuations through time
play no role in defining the ensemble. Ensembles are obtained by dividing a
huge rock sample into many mesoscopic volumes. Because rocks are a disordered
collection of grains in cohesive contact, we expect that once shear strain is
applied and cracks begin to arrive in the system, the mesoscopic volumes will
have a wide distribution of different crack states. These mesoscopic volumes
are the members of our ensembles. We determine the probability of observing a
mesoscopic volume to be in a given crack state by maximizing Shannon's measure
of the emergent crack disorder subject to constraints coming from the
energy-balance of brittle fracture. The laws of thermodynamics, the partition
function, and the quantification of temperature are obtained for such cracking
systems.
