物理学前沿学术报告：Solving the Problem of Absence of Detailed Balance and unification of dynamics near and far from equilibrium

主讲人：Ping Ao, PhD
　　　　Department of Mechanical Engineering and Department of Physics University of Washington, Seattle, WA 98195, USA

时间：2008年6月25日(星期三)下午14:00

地点：上海交通大学闵行校区物理实验楼报告厅

摘要：

The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in my seminar, 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. Here I present an exploration of the connection between thermodynamics and Darwinian dynamics and iscuss a few related topics. I will show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of  oltzmann–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 ontribute 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. The former naturally implies the recent arzynski equality. The latter provides the key to solve the renowned problem of absence of detailed balance. Such connection indicates 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, Hamiltonian dynamics, that dominates the physical sciences. Present exploration suggests the existence of a unified tochastic dynamical framework both near and far from equilibrium. The corresponding results may be particularly relevant in the current study of stochastic dynamics of nanosystems, and can be tested experimentally.