Title: Time-Irreversible Quantum-Classical Dynamics of Molecular Models in the Brain Show Chinese title

Title: 分子模型在大脑中的时间不可逆的量子经典动力学

Abstract: This manuscript aims to illustrate a quantum-classical dissipative theory (suited to be converted to effective algorithms for numerical simulations) within the long-term project of studying molecular processes in the brain. Other approaches, briefly sketched in the text, have advocated the need to deal with both quantum and classical dynamic variables when studying the brain. At variance with these other frameworks, the manuscript's formalism allows us to explicitly treat the classical dynamical variables. The theory must be dissipative not because of formal requirements but because brain processes appear to be dissipative at the molecular, physiological, and high functional levels. We discuss theoretically that using Brownian dynamics or the Nos\`e-Hoover-Chain thermostat to perform computer simulations provides an effective way to introduce an arrow of time for open quantum systems in a classical environment. In the future, We plan to study classical models of neurons and astrocytes, as well as their networks, coupled to quantum dynamical variables describing, e.g., nuclear and electron spins, HOMO and LUMO orbitals of phenyl and indole rings, ion channels, and tunneling protons. Show Chinese abstract

Abstract: 本手稿旨在阐述一种量子-经典耗散理论（适合转换为用于数值模拟的有效算法），这是研究大脑中分子过程长期项目的一部分。文中简要介绍了其他方法，这些方法主张在研究大脑时需要处理量子和经典动力变量。与这些其他框架不同，本手稿的形式主义使我们能够显式处理经典动力变量。该理论必须是耗散的，不是因为形式要求，而是因为大脑过程在分子、生理和高级功能层面似乎都是耗散的。我们从理论上讨论了使用布朗动力学或Nosè-Hoover-Chain恒温器进行计算机模拟，可以有效地为开放量子系统在经典环境中的时间箭头提供一种方法。未来，我们将研究神经元和星形胶质细胞的经典模型及其网络，以及它们与描述例如苯基和吲哚环的核和电子自旋、HOMO和LUMO轨道、离子通道和隧穿质子的量子动力变量的耦合。