I consider new liquid-state kinetic theories for particles with interaction potentials that are continuously varying (such as Lennard-Jones particles and inverse-power-law potentials), rather than discontinuous (such as the hard-sphere or square-well potentials). I do it by incorporating a stochastic smoothing term in the hard-core and square-well edge of the square-well kinetic model (KVTIII). The resulting kinetic model has built in conservation laws and trend to equilibrium (H-functional). I derive the virial and transport coefficients for the underlying fluid. I also consider existence and stability results for some of the corresponding systems of the integro-partial differential equations.
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