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Advances in High Energy Physics
Volume 2016 (2016), Article ID 5710625, 8 pages
http://dx.doi.org/10.1155/2016/5710625
Research Article

Thermodynamics of Acoustic Black Holes in Two Dimensions

School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

Received 12 May 2016; Accepted 11 July 2016

Academic Editor: Emmanuel N. Saridakis

Copyright © 2016 Baocheng Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

It is well-known that the thermal Hawking-like radiation can be emitted from the acoustic horizon, but the thermodynamic-like understanding for acoustic black holes was rarely made. In this paper, we will show that the kinematic connection can lead to the dynamic connection at the horizon between the fluid and gravitational models in two dimensions, which implies that there exists the thermodynamic-like description for acoustic black holes. Then, we discuss the first law of thermodynamics for the acoustic black hole via an intriguing connection between the gravitational-like dynamics of the acoustic horizon and thermodynamics. We obtain a universal form for the entropy of acoustic black holes, which has an interpretation similar to the entropic gravity. We also discuss the specific heat and find that the derivative of the velocity of background fluid can be regarded as a novel acoustic analogue of the two-dimensional dilaton potential, which interprets why the two-dimensional fluid dynamics can be connected to the gravitational dynamics but it is difficult for four-dimensional case. In particular, when a constraint is added for the fluid, the analogue of a Schwarzschild black hole can be realized.