Rutgers Discrete Mathematics Seminar

Title: Big Bang Theory

Speaker: Jozsef Beck, Rutgers

Date: Tuesday, February 28, 2012 2:00pm

Location: Hill Center, Room 124, Rutgers University, Busch Campus, Piscataway, NJ

Abstract: Statistical mechanics is based on the axiom that the gas molecules are independent random variables. Our goal is to justify this axiom in a Newtonian model. Consider N=10^{26} point-billiards in a cubic container of side length one meter. Let us start with an arbitrary extreme non-equilibrium initial configuration (=the set of starting points); for example, we can start with a Big Bang: when at the beginning all N point-billiards are in the same point. Assuming the point-billiards have ``typical initial velocities" with average speed 1000 meter per second (which is realistic), how long does it take, starting from a Big Bang (say), to reach square-root equilibrium? Is it less than a second or more than 100 years? The answer depends on the definition of ``typical initial velocities". (Square-root equilibrium means that, in a given test set, the number of point-billiards equals the expected number plus-minus the square-root of N; i.e., random size fluctuation.) We explain this, and other surprising facts.