Abstract:

We propose a probabilistic model for a natural law in physics: the Gibbsian statistical thermodynamics. Gibbs’ two separate theories, (i) macroscopic chemical thermodynamics and (ii) statistical mechanics, are unified under the new mathematics based on large deviation theory of iid samples.  Extending this model to Markovian samples, an attempt is made to view Lagrange-Hamilton-Jacobi formulation of Newtonian mechanics as a non-random signature via the most probable move into future, the maximal likely move in the past, and the most probable motions connecting past to future, even with time irreversibility.  These results suggest a pleasing answer to E. P. Wigner’s “unreasonable effectiveness of mathematics” as a classifier for recurrent motions rather than law(s) coming from the above.

Personal Website：https://amath.washington.edu/people/hong-qian

Recording: https://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Stochastic_Thermodynamics_Kinematics_and_Classical_Mechanics.html