The specific heat of non-equilibrium steady states

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Abstract
We derive two formally exact expressions for the temperature derivative of an arbitrary mechanical property of the non-equilibrium steady state. Applying these expressions to the internal energy, we obtain two formulae for the specific heat of the steady state. One of these shows that the specific heat can be calculated by analysing fluctuations in the steady state. The second formula relates the steady state specific heat to the transient response observed when an ensemble of equilibrium systems is perturbed by the field.