  Causal horizons in pure Poincare $AdS$ are Killing horizons generated by
dilatation vector. Renormalization group (RG) flow breaks the dilatation
symmetry and makes the horizons dynamical. We propose that the boundary RG flow
is dual to the thermodynamics of the causal horizon. As a check of our proposal
we show that the gravity dual of the boundary $c$-theorem is the second law of
thermodynamics obeyed by causal horizons. The holographic $c$-function is the
Bekenstein-Hawking entropy (density) of the dynamical causal horizon. We
explicitly construct the $c$-function in a generic class of RG-flow geometries
and show that it interpolates monotonically between the UV and IR central
charges as a result of the second law.
