Statistical mechanics in the femtosecond era

The probability assumptions currently used in non-equilibrium statistical mechanics were inherited from the nineteenth and early twentieth centuries. They work very well provided either that the system is either very close to equilibrium or that the time interval between observations is not too small -- for example, in a gas this time interval is, in effect, assumed to be large compared with the time necessary to execute a collision. The probability assumptions that are used for well enough separated observations have the implication that the successive observational states can be treated as a Markov process. But physical instrumentation has moved on, and in the twenty-first century we have to reckon with the possibility of much shorter time intervals between observations, for which the assumption of a Markov process is not tenable. This talk is about how to develop a general framework of statistical mechanics which does not require such an assumption.