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One-dimensional hard rod gases are explicitly constructed as the limits ofdiscrete systems: exclusion processes involving particles of arbitrary length.Those continuum many-body systems in general do not exhibit the samehydrodynamic properties as the underlying discrete models. Considering asexamples a hard rod gas with additional long-range interaction and thegeneralized asymmetric exclusion process for extended particles ($\ell$-ASEP),it is shown how a correspondence between continuous and discrete systems mustbe established instead. This opens up a new possibility to exactly predict thehydrodynamic behaviour of this continuum system under Eulerian scaling bysolving its discrete counterpart with analytical or numerical tools. As anillustration, simulations of the totally asymmetric exclusion process($\ell$-TASEP) are compared to analytical solutions of the model and applied tothe corresponding hard rod gas. The case of short-range interaction is treatedseparately.Comment: 19 pages, 8 figure

Hard rod gas with long-range interactions: Exact predictions for hydrodynamic properties of continuum systems from discrete models