Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 3, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP03(2017)010
Keywords
Black Holes; Classical Theories of Gravity
Categories
Funding
- National Natural Science Foundation of China [11605082]
- Natural Science Foundation of Guangdong Province, China [2016A030310363, 2016A030307051, 2015A030313789]
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We define a kind of heat engine via three-dimensional charged BTZ black holes. This case is quite subtle and needs to be more careful. The heat flow along the isochores does not equal to zero since the specific heat C-V not equal 0 and this point completely differs from the cases discussed before whose isochores and adiabats are identical. So one cannot simply apply the paradigm in the former literatures. However, if one introduces a new thermodynamic parameter associated with the renormalization length scale, the above problem can be solved. We obtain the analytical efficiency expression of the three-dimensional charged BTZ black hole heat engine for two different schemes. Moreover, we double check with the exact formula. Our result presents the first specific example for the sound correctness of the exact efficiency formula. We argue that the three-dimensional charged BTZ black hole can be viewed as a toy model for further investigation of holographic heat engine. Furthermore, we compare our result with that of the Carnot cycle and extend the former result to three-dimensional spacetime. In this sense, the result in this paper would be complementary to those obtained in four-dimensional spacetime or ever higher. Last but not the least, the heat engine efficiency discussed in this paper may serve as a criterion to discriminate the two thermodynamic approaches introduced in ref. [29] and our result seems to support the approach which introduces a new thermodynamic parameter R = r(0).
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