  In this article we derive Harnack estimates for conjugate heat kernel in an
abstract geometric flow. Our calculation involves a correction term D. When D
is nonnegative, we are able to obtain a Harnack inequality. Our abstract
formulation provides a unified framework for some known results, in particular
including corresponding results of Ni, Perelman, and Tran as special cases.
Moreover it leads to new results in the setting of Ricci-Harmonic flow and mean
curvature flow in Lorentzian manifolds with nonnegative sectional curvature.
