Optimal Control Theory of the (2+1)-Dimensional BTZ Black Hole

TL;DR

This paper develops a geometric optimal control framework for the (2+1)-dimensional BTZ black hole, enabling the analysis of thermodynamic processes and fluctuations through geodesic trajectories that optimize entropy or energy transfer.

Contribution

It introduces the first geometric optimal control theory tailored for the BTZ black hole, linking thermodynamic state transitions with extremal entropy production or dissipation.

Findings

Constructed geodesic trajectories for thermodynamic processes

Formulated finite-time optimal protocols for black hole thermodynamics

Provided a new geometric perspective on black hole thermodynamic fluctuations

Abstract

We apply a finite-time geometric optimization framework to investigate thermal fluctuations and (non)equilibrium optimal processes in the $(2+1)$-dimensional BTZ black hole. Employing Hessian thermodynamic information metrics, we construct geodesic trajectories that define optimal protocols connecting distinct thermodynamic configurations. Finite-time state transitions are described by paths that extremize entropy production or energy dissipation, depending on the chosen thermodynamic representation. This work presents the first formulation of a geometric optimal control theory for the BTZ black hole.