In a non-flat Friedmann universe, the unified first law dE = TdS + WdV and the energy-flux form -dE = TdS are consistent only when the horizon volume is taken as the areal volume, not the proper invariant volume.
First law of thermodynamics and Friedmann-like equations in braneworld cosmology
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abstract
We derive the Friedmann-like equations in braneworld cosmology by imposing the first law of thermodynamics and Bekenstein's area-entropy formula on the apparent horizon of a Friedmann-Roberston-Walker universe in both Randall-Sundrum II gravity and Dvali-Gabadadze-Porrati gravity models. Israel's boundary condition plays an important role in our calculations in both cases, besides the first law of thermodynamics and Bekenstein's area-entropy formula. The results indicate that thermodynamics on the brane world knows the behaviors of gravity.
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gr-qc 1years
2019 1verdicts
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First Law of Thermodynamics and Emergence of Cosmic Space in a Non-Flat Universe
In a non-flat Friedmann universe, the unified first law dE = TdS + WdV and the energy-flux form -dE = TdS are consistent only when the horizon volume is taken as the areal volume, not the proper invariant volume.