Statistical mechanics of cracks

This paper describes a formalism designed to answer questions about Hamiltonian systems in contact with a heat bath. The formalism is applied to a simple model of fracture to find, first, the rate at which a crack creeps through a brittle body as a result of thermal fluctuations and, second, the rate at which the crack jumps from creeping to rapid motion. The dominant exponential behavior of these processes is calculated exactly, but the prefactors are only estimated. Some of the solutions cannot be viewed in the traditional manner as corresponding to passage over a saddle point. Viewed as an isolated Hamiltonian system, the crack shows that irreversible behavior can arise because, although the probability of traveling from past to present equals the probability of traveling backwards from present to past, the probability of traveling still further into the future is exponentially greater.