Abstract
The exact formula for the equilibrium one-dimensional binary distribution function for scalar particles, interacting by the potential 1/r, is obtained in the post-Galilean approximation. To take into account the post-Galilean corrections (i.e. the values of the order of O(c−2), where c is the velocity of light), the temperature shift is suggested. It means that in this relativistic approximation we can use the classical coordinate distribution function with the shifted temperature parameter.We also calculate the configuration integral of this system in the thermodynamic limit in the nearest neighbour approximation.
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