Nonequilibrium transport and thermodynamics in driven lattice gases

驱动晶格气体提供了概念上简单的模型，用于研究远离平衡的相互作用粒子的输运。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在相邻的晶格位置之间移动。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，通过细胞膜的离子传输，通过纳米孔的分子运动，以及沿着细胞中的细丝的马达蛋白质的传输。这个研究项目包括三个部分，其中目前的问题的非平衡物理的驱动晶格气体及其连接到空间连续动力学的解决。在第一部分中，考虑格子气模型，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根据含时密度泛函理论确定。的质量的理论预测进行检查对动力学蒙特卡罗模拟。在与环境交换粒子的开放系统中，应研究非平衡稳态之间的相变。在这些相变中，内部状态的平均占用数突然改变或它们对控制参数的依赖性。一个进一步的重点是针对的问题，是否有限的颗粒尺寸的影响，在连续空间动力学中看到的，可以捕获在晶格气模型。在第二部分中，电流进行了研究，这是由于粒子相互作用的流动对外部驱动。这种驱动可以是恒定的阻力，也可以是随时间变化的力。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已经发现了电流反转，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。第三部分是关于在外力的微小变化下，粒子流、能量流和热流等不同类型的流的变化。应探讨某些非平衡状态（其中不同类型电流的响应表现出对称性）是否在热力学性质方面具有特定意义。

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.