Cedric Igelspacher

OS Mathematical Physics December 2 14:30

From Normalizable to Non-Normalizable Measures: a Survey through the Boltzmannian Paradigm

The talk adresses two conflicts:

First, why is there irreversible macroscopic behavior in nature that is grounded in the microscopic dynamics being reversible. To answer this we will first go through the statistical account of Boltzmann clearing up this conflict between time-symmetric and time-asymmetric behavior as being typical. Low-entropy states evolve towards high-entropy states. After that we try to see how in the same setting the origin of low-entropy states can be explained by discussing the Boltzmann fluctuation scenario as well as the Past Hypothesis. The problems that arise through these leads us to a proposal made by Carroll and Chen which allows us to establish an arrow of time as a typical feature of our universe. However by doing this, we have to assume that the entropy can grow unbounded, hence the microcanonical measure becomes non-normalizable.

Second, reasoning in Boltzmann’s way given the macrostate now, we should expect entropy to grow in both time directions. This seems uncompatible within a model that assumes entropy to be unbounded. We will see how this conflict can be resolved. After that we look at different kinds of reasoning that mainly rely on the fact that only a theory with unbounded entropy can give solid epistemic ground that is in accordance with us being ordinary observers and not boltzmann brains.