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Explore the mathematical foundations of biochemical reaction dynamics in this 44-minute conference talk that examines macroscopic behaviors of nonequilibrium systems from a Hamiltonian perspective. Discover how biochemical reactions in living cells operate as open systems that exchange energy and materials with their surroundings, and learn about the mesoscopic modeling approach using random time-changed Poisson processes to represent chemical quantities. Delve into the thermodynamic limit where large deviation rate functions from chemical master equations are governed by Hamilton-Jacobi equations, and understand the decomposition of macroscopic reaction rate equations into Onsager-type strong gradient flows with conservative dynamics. Gain insights into large deviation principles and importance sampling techniques for analyzing transition paths between metastable states in chemical reactions, providing a comprehensive mathematical framework for understanding complex biochemical processes.
