Fidelity Susceptibility as Holographic PV-Criticality

It is well known that entropy can be used to holographically establish a connection between geometry, thermodynamics and information theory. In this paper, we will use complexity to holographically establish a connection between geometry, thermodynamics and information theory. Thus, we will analyse the relation between holographic complexity, fidelity susceptibility, and thermodynamics in extended phase space. We will demonstrate that fidelity susceptibility (which is the informational complexity dual to a maximum volume in AdS) can be related to the thermodynamical volume (which is conjugate to the cosmological constant in the extended thermodynamic phase space). Thus, this letter establishes a relation between geometry, thermodynamics, and information theory, using complexity.