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f(R) Black Holes as Heat Engines

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Abstract

With the cosmological constant considered as a thermodynamic variable in the extended phase space, it is natural to study the thermodynamic cycles of the black hole, which is conjectured to be performed using renormalization group flow. We first investigate the thermodynamic cycles of a 4-dimensional asymptotically AdS f(R) black hole. Then we study the thermodynamic cycles of higher dimensional asymptotically AdS f(R) black holes. It is found that when ΔV ≪ ΔP, the efficiency of isobar-isochore cycles running between high temperature T H and low temperature T C will increase to its maximum value, which is exactly the Carnot cycles’ efficiency both in 4-dimensional and in higher dimensional cases. We speculate that this property is universal for AdS black holes, if there is no phase transition in the thermodynamic cycle. This result may deepen our understanding of the thermodynamics of the AdS black holes.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11235003, 11175019, and 11178007).

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Authors and Affiliations

  1. Department of Physics, Institute of Theoretical Physics, Beijing Normal University, Beijing, 100875, China

    Ming Zhang & Wen-Biao Liu

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  1. Ming Zhang
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  2. Wen-Biao Liu
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Correspondence to Wen-Biao Liu.

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Zhang, M., Liu, WB. f(R) Black Holes as Heat Engines. Int J Theor Phys 55, 5136–5145 (2016). https://doi.org/10.1007/s10773-016-3134-4

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  • DOI: https://doi.org/10.1007/s10773-016-3134-4

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