  Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at
long distances. We study this theory on a four- and three-torus, and
analytically argue the existence of a large-small volume equivalence. For any
finite mass, center symmetry unbroken phase exists at sufficiently small volume
and this phase can be used to study the large-volume limit through the
Eguchi-Kawai equivalence. A finite temperature version of volume independence
implies that thermodynamics on R^3 x S^1 can be studied via a unitary matrix
quantum mechanics on S^1, by varying the temperature. To confirm this
non-perturbatively, we numerically study both zero- and one-dimensional
theories by using Monte-Carlo simulation. Order of finite-N corrections turns
out to be 1/N. We introduce various twisted versions of the reduced QCD which
systematically suppress finite-N corrections. Using a twisted model, we observe
the confinement/deconfinement transition on a 1^3 x 2-lattice. The result
agrees with large volume simulations of Yang-Mills theory. We also comment that
the twisted model can serve as a non-perturbative formulation of the
non-commutative Yang-Mills theory.
