Membrane configurations in the Banks-Fischler-Shenker-Susskind matrix model are unstable due to the existence of flat directions in the potential and the decay process can be seen as a realization of chaotic scattering. In this note, we compute the lifetime of a membrane in a reduced model. The resulting lifetime exhibits scaling laws with respect to energy, coupling constant and a cut-off scale. We numerically evaluate the scaling exponents, which cannot be fixed by the dimensional analysis. Finally, some applications of the results are discussed.

Japan

Osamu Fukushima

Tomohiro Shigemura

Kentaroh Yoshida

Scaling law for membrane lifetime

We propose a formulation of black hole thermodynamics that incorporates the notions of heat and work, based on the thermodynamics in quantum theory and the AdS/CFT correspondence. First, for coupled holographic CFTs, we define a coarse-graining procedure adopting the principle of maximum entropy. Employing this approach, when the system is divided into a target system and thermal baths, we formulate the first and second laws, as well as the fundamental thermodynamic relation. Then, by translating the resulting thermodynamics into the AdS gravity language, we construct a thermodynamic framework for composite black hole systems that encompasses both heat and work. This formulation relies on holography, but not on energy conditions on the gravity side. We also argue that the second law serves as a necessary criterion for the UV completeness of gravitational theories.