We define thermodynamic pressure P by work density W as the conjugate quantity of thermodynamic volume V from field equation. We derive the equations of state P = P ( V , T ) for the Friedmann–Robertson–Walker (FRW) universe in Einstein gravity and a modified gravity respectively. We find that the equation of state from Einstein gravity shows no P - V phase transition, while the equation of state from the modified gravity does, where the critical exponents are the same as those in mean field theory.
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Kong et al. (2022) studied this question.
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