Eur. Phys. J. C (2018) 78: 765
https://doi.org/10.1140/epjc/s10052-018-6226-x

Regular Article - Theoretical Physics

Thermodynamic and holographic information dual to volume

¹ Department of Physics, College of Science, Sultan Qaboos University, P.O. Box 36, Al-Khodh 123, Muscat, Sultanate of Oman
² Irving K. Barber School of Arts and Sciences, University of British Columbia Okanagan, Kelowna, BC, V1V 1V7, Canada
³ Department of Physics and Astronomy, University of Lethbridge, Lethbridge, AB, T1K 3M4, Canada
⁴ Department of Physics and Astronomy, College of Science King Saud University, Riyadh, 11451, Saudi Arabia
⁵ Université Clermont Auvergne, 4 Avenue Blaise Pascal, 63710, Aubière, France
⁶ Physics Department, Nazarbayev University, Astana, Kazakhstan
⁷ Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana, 010008, Kazakhstan

^* e-mail: davood@squ.edu.om

Received: 28 December 2017
Accepted: 10 September 2018
Published online: 22 September 2018

Abstract

In this paper, we will analyze the connection between the fidelity susceptibility, the holographic complexity and the thermodynamic volume. We will regularize the fidelity susceptibility and the holographic complexity by subtracting the contribution of the background AdS spacetime from the deformation of the AdS spacetime. It will be demonstrated that this regularized fidelity susceptibility has the same behavior as the thermodynamic volume and that the regularized complexity has a very different behavior. As the information dual to different volumes in the bulk would be measured by the fidelity susceptibility and the holographic complexity, this paper will establish a connection between thermodynamics and information dual to a volume.