Null surface thermodynamics in topologically massive gravity

We study three dimensional topologically massive gravity (TMG) in presence of a generic codimension one null boundary. The existence of the boundary is accounted for by enlarging the Hilbert space of the theory by degrees of freedom which only reside at the boundary, the boundary degrees of freedom. The solution phase space of this theory in addition to bulk massive chiral gravitons of the TMG, involves boundary modes which are labeled by surface charges associated with large diffeomorphisms. We show boundary degrees of freedom obey a local thermodynamic description over the solution phase space, null surface thermodynamics, described by a local version of the first law, a local Gibbs-Duhem equation, and local zeroth law. Due to the expansion of the boundary and also the passage of the bulk mode through the boundary, our null surface thermodynamics describes an open boundary system that is generically out of thermal equilibrium.

Automated summary

We study the three dimensional topologically massive gravity (TMG) with a generic codimension one null boundary. The existence of the boundary is accounted for by introducing degrees of freedom that reside only at the boundary, known as boundary degrees of freedom, in the Hilbert space of the theory. The solution phase space of this theory involves both bulk massive chiral gravitons of TMG and boundary modes labeled by surface charges associated with large diffeomorphisms. We demonstrate that the boundary degrees of freedom obey a local thermodynamic description, known as null surface thermodynamics, which is described by a local version of the first law, a local Gibbs-Duhem equation, and local zeroth law. This null surface thermodynamics describes an open boundary system that is generically out of thermal equilibrium due to the expansion of the boundary and the passage of the bulk mode through the boundary.