  Weathering of silicate rocks at a planetary surface can draw down CO$_2$ from
the atmosphere for eventual burial and long-term storage in the planetary
interior. This process is thought to provide an essential negative feedback to
the carbonate-silicate cycle (carbon cycle) to maintain clement climates on
Earth and potentially similar temperate exoplanets. We implement thermodynamics
to determine weathering rates as a function of surface lithology (rock type).
These rates provide upper limits that allow estimating the maximum rate of
weathering in regulating climate. This modeling shows that the weathering of
mineral assemblages in a given rock, rather than individual minerals, is
crucial to determine weathering rates at planetary surfaces. By implementing a
fluid-transport controlled approach, we further mimic chemical kinetics and
thermodynamics to determine weathering rates for three types of rocks inspired
by the lithologies of Earth's continental and oceanic crust, and its upper
mantle. We find that thermodynamic weathering rates of a continental crust-like
lithology are about one to two orders of magnitude lower than those of a
lithology characteristic of the oceanic crust. We show that when the CO$_2$
partial pressure decreases or surface temperature increases, thermodynamics
rather than kinetics exerts a strong control on weathering. The kinetically-
and thermodynamically-limited regimes of weathering depend on lithology,
whereas, the supply-limited weathering is independent of lithology. Our results
imply that the temperature-sensitivity of thermodynamically-limited silicate
weathering may instigate a positive feedback to the carbon cycle, in which the
weathering rate decreases as the surface temperature increases.
