Heat engine in the three-dimensional spacetime

Abstract

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 $C_V\ne 0$ 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 $R=r_0$.

Revised version. Discussions added

References in corpus (16)

• The Black Hole in Three Dimensional Space Time
• P-V criticality of charged AdS black holes
• Enthalpy and the Mechanics of AdS Black Holes
• Thermodynamics of Kerr-Newman-AdS Black Holes and Conformal Field Theories
• Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization
• Pressure and volume in the first law of black hole thermodynamics
• The cosmological constant and the black hole equation of state
• Multiple Reentrant Phase Transitions and Triple Points in Lovelock Thermodynamics
• Holographic Heat Engines
• Kerr-AdS analogue of triple point and solid/liquid/gas phase transition
• Holographic entanglement entropy and the extended phase structure of STU black holes
• Reentrant phase transitions and van der Waals behaviour for hairy black holes
• Born-Infeld AdS Black Holes as Heat Engines
• Gauss-Bonnet Black Holes and Holographic Heat Engines Beyond Large N
• An Exact Efficiency Formula for Holographic Heat Engines
• Microscopic entropy of the charged BTZ black hole

Cited by in corpus (26)

• Regular black holes: A short topic review
• Joule-Thomson Expansion of Kerr-AdS Black Holes
• Thermodynamics of charged accelerating AdS black holes and holographic heat engines
• Accelerating AdS black holes as the holographic heat engines in a benchmarking scheme
• A Note on Critical Nonlinearly Charged Black Holes
• Instability of Super-Entropic Black Holes in Extended Thermodynamics
• Thermal Stability, P-V Criticality and Heat Engine of Charged Rotating Accelerating Black Holes
• Regular Bardeen AdS Black Hole as a Heat Engine
• Black Hole Chemistry: the first 15 years
• Benchmarking Black Hole Heat Engines, II
• Holographic Heat engine within the framework of massive gravity
• Phase transition and heat engine efficiency of phantom AdS black holes
• Thermodynamic schemes of charged BTZ-like black holes in arbitrary dimensions
• Holographic heat engine with momentum relaxation
• Phantom RN-AdS black holes in noncommutative space
• Modified Cosmic Chaplygin AdS Black Hole
• Holographic heat engine in Horndeski model with the $k$-essence sector
• Massive gravity with Lorentz symmetry breaking: black holes as heat engines
• A Note on Gauss-Bonnet Black Holes at Criticality
• Thermodynamics of 2+1 dimensional Coulomb-Like Black Holes from Non Linear Electrodynamics with a traceless energy momentum tensor
• Critical Heat Engines in Massive Gravity
• Topological Mod(A)Max AdS black holes
• Holographic Entanglement Entropy and Van der Waals transitions in Einstein-Maxwell-dilaton theory
• Magnetic black holes in 4$D$ Einstein--Gauss--Bonnet massive gravity coupled to nonlinear electrodynamics
• Holographic Heat Engines Coupled with Logarithmic $U(1)$ Gauge Theory
• Optical and Thermodynamic Signatures of Lorentz Symmetry Breaking in Bumblebee AdS Black Holes