In this article we derive the Bekenstein-Hawking formula of black hole entropy from a single long string. We consider a open string in the Rindler metric which can be obtained in the large mass limit from the Schwarzschild black hole metric. By solving the field equations we find a nontrivial solution with the exact value of the Hawking temperature. We see that this solution gives us the Bekens...

This paper introduces Markov chains and processes over nonabelian free groups and semigroups. We prove a formula for the f -invariant of a Markov chain over a free group in terms of transition matrices that parallels the classical formula for the entropy a Markov chain. Applications include free group analogues of the AbramovRohlin formula for skew-product actions and Yuzvinskii’s addition form...