In exactly solvable 1D fluids, negative thermal expansion arises for smooth potentials with positive third derivative and for potentials with a non-analyticity inside the attraction well, while quantized hard rods show no anomaly.
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Low-temperature anomalies in one-dimensional exactly solvable fluids
In exactly solvable 1D fluids, negative thermal expansion arises for smooth potentials with positive third derivative and for potentials with a non-analyticity inside the attraction well, while quantized hard rods show no anomaly.