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The evolutionary dynamics first conceived by Darwin and Wallace, Darwinian dynamics for short, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. During my talk I demonstration from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. The enabling tool is a new math structure for stochastic processes discovered recently, which will be explained. I will show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann–Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach: One is based on Feynman–Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. I will reason that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. It suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.
敖平教授. 1983年毕业于北京大学物理系后赴美留学. 师从 AJ Leggett 研学宏观量子现象和量子力学的测量问题, 获物理学博士学位, 博士后就教于 DJ Thouless, 研究拓扑缺陷的运动及其物理特性. 1999年后转入生物、医学 领域, 与 LE Hood 等投身于系统生物学研究, 侧重于癌症等方面的探索, 发展了新的癌症、代谢网络理论的计算平台, 研究复杂生物现象的机理和寻找新的疾病治疗、预防途径, 并发展相应的生物学基础理论——演化方程. 目前从事物理、工程、生物、医学研究.