A microscopic model for explaining the arrow of time

• Applicant: Professor Dr. Peter Pickl
• Subject Area: Mathematics ; Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2019 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 417613818

Since Boltzmann´s works there is the question of explaining the arrow of time in statistical physics: While the microscopic world does not know a direction of time, one experiences an arrow of time in the macroscopic world. Glass shatters when it falls on the ground whereas we do never see the reverse process. The usual explanations for that are based on a very special initial condition, a state of very high order which under the dynamics evolves in a natural way into a state of higher disorder. Here one can see (order -> disorder) the asymmetry in the propagation in time. This explanation, however, shifts the problem to the question where the initial state of high order came from.The project we propose will add an important argument to that discussion by analyzing a model for which for almost any initial state a growth in the disorder can be proven with mathematical rigor. Our focus lies in finding a model where our statements can be made rigorous at the price of slightly deviating from the models typically used to describe our universe. The goal is to find a principal argument that shows that the growth in disorder can be explained without assuming a special initial condition. The basic idea of our prove relies on a work of Antonov.

• DFG Programme: Research Grants