Nonequilibrium transport and thermodynamics in driven lattice gases

驱动格子气体为研究远离平衡的相互作用粒子的输运提供了概念上的简单模型。在这些模型中，粒子通过执行通常由主要空间连续运动的粗粒化引起的过渡来在相邻晶格位置之间移动。晶格气体模型可以应用于分子尺度上的各种非平衡过程，例如，离子通过细胞膜的传输，分子通过纳米孔的运动，以及细胞内马达蛋白沿细丝的传输。这项研究项目包括三个部分，其中解决了当前驱动格子气体的非平衡物理问题及其与空间连续动力学的联系。在第一部分中，考虑了格子气体模型，其中粒子可以处于不同的内部状态。对于这类扩展的模型，非平衡态的粒子密度和电流应基于随时间变化的密度泛函理论确定。用动力学蒙特卡罗模拟检验了理论预测的质量。在与环境交换粒子的开放系统中，需要研究非平衡稳态之间的相变。在这些相变过程中，内态的平均占有数发生突变或对控制参数的依赖关系。另一个焦点指向这样一个问题，即在连续空间动力学中看到的有限粒子大小的影响是否可以在晶格气体模型中捕捉到。在第二部分中，研究了粒子相互作用在外力作用下流动的电流。这种驱动可以是恒定的阻力，也可以是依赖时间的强迫。意外的电流方向通常被称为电流反转。在具有离散和连续空间动力学的系统中都发现了电流反转，其起源部分令人费解。基于总熵产生计算的理论处理将在共同的基础上解释它们的发生。第三部分讨论了不同类型的电流，如粒子电流、能量电流和热量电流在外部驱动力的微小变化下的变化。应探讨不同类型电流的响应呈现对称性的某些非平衡态在热力学性质方面是否具有特殊意义。

Driven lattice gases provide conceptually simple models for studying transport of interacting particles far from equilibrium. In these models, particles move between neighboring lattice sites by performing transitions that frequently result from a coarse-graining of primarily space-continuous movements. Lattice gas models can be applied to various nonequilibrium processes on molecular scales, as, for example, ion transport through cell membranes, motion of molecules through nanopores, and transport of motor proteins along filaments in cells. This research project comprises three parts, in which current problems of the nonequilibrium physics of driven latttice gases and their connection to space-continuous dynamics are tackled. In the first part, lattice gas models are considered, where particles can be in different internal states. For this extended class of models, particle densities and currents in nonequilibrium states shall be determined based on time-dependent density functional theory. The quality of the theoretical prediction is checked against kinetic Monte Carlo simulations. In open systems exchanging particles with their environment, phase transitions between nonequilibrium steady states shall be investigated. At these phase transitions, mean occupation numbers of internal states change abruptly or their dependence on control parameters. A further focus is directed towards the question, whether effects of a finite particle size, as seen in continuous space dynamics, can be captured in lattice gas models. In the second part, currents are investigated, which due to particle interactions flow against an external driving. This driving can be a constant drag or a time-dependent forcing. The unexpected current direction is often referred to as current reversal. Current reversals have been found in systems with both discrete and continuous space dynamics and their origin is partly puzzling. A theoretical treatment based on calculations of total entropy production shall explain their occurrence on a common footing. The third part concerns the change of different types of currents, as those of particles, energy and heat, under slight variations of external driving forces. It shall be explored, whether certain nonequilibrium states, where the response of different types of currents exhibits a symmetry, have a particular meaning in terms of thermodynamic properties.