  Ramp compression experiments characterize high-pressure states of matter at
temperatures well below those present in shock compression. However, because
temperature is typically not directly measured during ramp compression, it is
uncertain how much heating occurs under these shock-free conditions. Here, we
performed a series of ab initio simulations on carbon in order to match the
density-stress measurements of Smith et al. [Smith, et al., Nature 511, 330
(2014)]. We considered isotropically as well as uniaxially compressed solid
carbon in the diamond and BC8 phases, with and without defects, as well as
liquid carbon. Our idealized model ascribes heating during ramp compression to
an initially uniaxially compressed cell transforming isochorically into an
isotropically (hydrostatic equivalent) compressed state having lower internal
energy, hence higher temperature so as to conserve energy. Multiple such
heating events can occur during a single ramp experiment, leading to higher
temperatures than with isentropic compression. Comparison with experiments
shows that heating alone does not explain the equation of state measurements on
diamond, instead implying that a significant uniaxial stress component remains
present at high compression. The temperature predictions of our ramp
compression model remain to be verified with future laboratory measurements.
