  Nonequilibrium kinetic effects are widespread in fluid systems and might have
a significant impact on the inertial confinement fusion ignition process, and
the entropy production rate is a key factor in accessing the compression
process. In this work, we study the Richtmyer-Meshkov instability (RMI) and the
reshock process by a two-fluid discrete Boltzmann method (DBM). Firstly, the
DBM result for the perturbation amplitude evolution is in good agreement with
that of experiment. Greatly different from the case of normal shocking on
unperturbed plane interface between two uniform media, in the RMI case, the
Thermodynamic Non-Equilibrium (TNE) quantities show complex but inspiring
kinetic effects in the shocking process and behind the shock front. The kinetic
effects are detected by two sets of TNE quantities. The first set are $\left
|\Delta _{2}^{ {\rm{*}}}\right |$,$\left |\Delta _{3,1}^{ {\rm{*}}}\right |$,
$\left | \Delta _{3}^{ {\rm{*}}}\right |$, and $\left |\Delta _{4,2}^{
{\rm{*}}}\right |$. All the four TNE measures abruptly increase in the shocking
process. $\left |\Delta _{3,1}^{ {\rm{*}}}\right |$ and $\left |\Delta _{3}^{
{\rm{*}}}\right |$ show similar behaviors. They continue to increase in a much
lower rate behind the shock front. $\left |\Delta _{2}^{ {\rm{*}}}\right |$ and
$\left |\Delta _{4,2}^{ {\rm{*}}}\right |$ have different dimensions, but show
similar behaviors. They quickly decrease to be very small behind the shock
front. The second set of TNE quantities are ${\dot{S} _{NOMF}}$, ${\dot{S}
_{NOEF}}$ and ${\dot{S} _{sum}}$. It is found that the mixing zone is the
primary contribution region to the ${\dot{S} _{NOEF}}$, while the flow field
region excluding mixing zone is the primary contribution region to the
${\dot{S} _{NOMF}}$. The light fluid has a higher entropy production rate than
the heavy fluid.
