Thermodynamics of acoustic black holes in two dimensions

TL;DR

This paper explores the thermodynamic properties of two-dimensional acoustic black holes, establishing a connection between fluid dynamics and gravitational models, and deriving a universal entropy form with implications for analogue gravity.

Contribution

It introduces a thermodynamic-like framework for 2D acoustic black holes, linking fluid dynamics to gravitational thermodynamics and deriving a universal entropy expression.

Findings

Thermodynamic-like description for 2D acoustic black holes established.

Universal entropy form similar to entropic gravity derived.

Connection between fluid velocity derivative and 2D dilaton potential identified.

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 dimension, 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 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.