Energy of Decomposition and Entanglement Thermodynamics for $T^2$-deformation

TL;DR

This paper develops laws of entanglement thermodynamics for $T^2$-deformed theories, revealing how entanglement entropy changes relate to energy and unitarity, using holography across dimensions.

Contribution

It introduces a set of entanglement thermodynamics laws for $T^2$-deformed theories, including a new interpretation of energy as decomposition energy, and extends the framework holographically to higher dimensions.

Findings

First law links entanglement entropy change to bending energy.

Second law implies an inequality ensuring unitarity.

Third law defines the deformation temperature.

Abstract

We have presented a set of laws of entanglement thermodynamics for $T\bar{T}$-deformed CFTs and in general for $T^2$-deformed field theories. In particular, the first law of this set, states that although we are dealing with a non-trivial deformed theory, the change of the entanglement entropy is simply translated to the change of the bending energy of the entangling surface. We interpret this energy as the energy of decomposition. Probing the whole spectrum of the deformed theory, a second law also results, which suggests an inequality that the first law is derived from its saturation limit. We explain that this second law guarantees the preservation of the unitarity bound. The thermodynamical form of these laws requires us to define the temperature of deformation and express its characteristics, which is the subject of the third law. We use a holographic approach in this analysis and in each case, we consider the generalization to higher dimensions.