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An equation of state (abbreviated EoS) relates temperature, pressure, and volume of a substance. Boyle's law, from the 1600s is the original example: that given a gas of constant temperature, the pressure and volume are inversely proportional. Equations of state are examples of constitutive equations (or constitutive relations), equations describing the behavior of a material, The term equation of state is commonly used in some fields, often for gases. For solids, other terms for constitutive equations are also commonly used, including those describing the effects of stress, such as under what conditions and how much such material bends.
An equation of state of a gas, in effect, depends upon its partition function.
The terms soft versus hard (or stiff) refer to a characteristic of the equation of state: soft means pressure varies weakly with density and hard or stiff means pressure varies strongly with density.