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A toy-model is used for describing the steps achieving the no-reversibledirection axiom in a tutorial manner: i) choice of a state space results in the balance equations on state space which are linear in the process directions, ii) a reversible process direction cannot be generated by combination of non-reversible ones, iii) process directions which are in the kernel of the balance equations do not enter the entropy production. The Coleman-Mizel formulation of the second law and the Liu relations follow immediately.

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The structure of a fluid of hard Gaussian overlap particles of elongation κ = 5, confined between two hard walls, has been calculated from density-functional theory and Monte Carlo simulations. By using the exact expression for the excluded volume kernel (Velasco E and Mederos L 1998 J. Chem. Phys. 109 2361) and solving the appropriate Euler-Lagrange equation entirely numerically, we have been able to extend our theoretical predictions into the nematic phase, which had up till now remained relatively unexplored due to the high computational cost. Simulation reveals a rich adsorption behaviour with increasing bulk density, which is described semi-quantitatively by the theory without any adjustable parameters.