Date: October 20, 2021
Time: 3:30 PM
Title: How to cook very small eggs: The microscopic onset of irreversibility
We consider irreversibility in the sense of cooking an egg. One turns the heat up, then back down, but the egg does not return to its initial raw state, even if the heating and cooling is arbitrarily slow and gradual. Instead the slow external parameter change induces a spontaneous transition to a qualitatively different cooked state, and this transition is not undone by undoing the slow parameter change that caused it.
Analogous processes can be defined for any dynamical system, so what is the microscopic limit of this egg-cooking form of irreversibility? One might suppose that microscopic analogs of “raw” and “cooked” states exist, but differ from each other only infinitesimally in the microscopic limit, with the difference becoming greater with increasing system size. We show with explicit examples that this need not be the case: after an arbitrarily slow forward-and-back parameter sweep, even a single degree of freedom can return to a final state drastically different from its initial state. Whether this “cooking” transition happens depends sensitively on initial conditions, however. What increases with system size is the fraction of initial states for which the irreversible transition occurs. When small eggs become cooked, they are just as thoroughly cooked as macroscopic eggs, but the chance of cooking a small egg is small.
After presenting that minimal example I will use slightly more complicated models to illustrate possible additional effects of quantum mechanics and dynamical chaos in the microscopic onset of irreversibility.
Institution: Technische Universität Kaiserslautern
Host: Dr. Sung-Sik Lee & Duncan O'Dell