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I know that is part of the definition of the notion of a state variable, but i guess that definition its made to suit the actual materials of experiments, like the measurement equipment. Why can't temperature or volume get measured on a system that's out of equilibrium? Thank you for your time.

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You can certainly measure volume of a system out of equilibrium. Temperature is trickier, since a system out of equilibrium might have different temperatures at different places, but you can measure that, too. Or, it might have different temperatures for different degrees of freedom: a plasma, for example, often has different electron and ion temperatures. And there may be substantial non-thermal energy, in the form of waves, for example. All of these may be measured. However, the more complicated the deviations from equilibrium are, the harder it is to apply thermodynamic ideas to the system.

"Thermodynamics doesn't work in plasmas." - Bruno Coppi

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