分隔系统克努森热力学中的熵产生
Entropy production in Knudsen thermodynamics of compartmented systems
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中文总结 AI 辅助
研究分隔系统中克努森气体的熵产生与非平衡输运，通过随机动力系统建模，利用互易假设简化熵产生率定义，采用模块化分析和马尔可夫链等方法，以系列示例揭示热棘轮效应，给出封闭形式表达式。
中文摘要 AI 辅助
我们研究了一类模拟限制在分隔容器中的克努森气体的随机动力系统中的熵产生和非平衡输运。该系统由单个进行随机台球运动的粒子组成，碰撞导致通过半反射、分隔壁的随机反射或透射。首先将稳态熵产生率表示为正向和时间反转路径测度之间的相对熵。在用于将温度引入一般随机台球系统的互易假设下，展示了这种信息论定义如何简化为经典热力学公式：传递到壁的平均能量除以其局部温度，即随机克劳修斯关系。然后我们对分隔系统进行模块化分析。每个开放隔室由隔室散射算子及其逗留统计来表征。隔室入口状态序列定义了一个马尔可夫链，其稳态分布用于更新奖励定理中，以将隔室贡献组装成全局熵产生率。通过一系列由广义麦克斯韦 - 斯莫卢霍夫斯基散射算子控制且易于详细明确分析的复杂度递增的示例来说明该框架。此类算子由几个参数定义：温度、部分热适应、势垒高度和孔隙率系数。核心示例是由两个不同温度的热壁和一个势垒组成的循环三室系统。对于完全热适应，我们获得了熵产生率和循环净概率环流的封闭形式表达式，揭示了类似于热渗透的热棘轮效应。
英文摘要
We investigate entropy production and nonequilibrium transport in a class of random dynamical systems modeling a Knudsen gas confined to a compartmented container. The system consists of a single particle undergoing random billiard motion, with collisions leading to random reflection or transmission through semi-reflecting, compartment-separating walls. The stationary entropy production rate is first expressed as the relative entropy between forward and time-reversed path measures. Under a reciprocity assumption, used to introduce temperature into the general random billiard system, it is shown how this information-theoretic definition reduces to the classical thermodynamic formula: the mean energy transferred to the walls divided by their local temperatures, a stochastic Clausius relation. We then develop a modular analysis of compartmented systems. Each open compartment is characterized by a compartment scattering operator and its sojourn statistics. The sequence of compartment entrance states defines a Markov chain whose stationary distribution is used in a renewal-reward theorem to assemble the compartment contributions into the global entropy production rate. The framework is illustrated with a series of examples of increasing complexity governed by a generalized Maxwell-Smoluchowski scattering operator and amenable to detailed and explicit analysis. Such operators are defined by a few parameters: temperature, a partial thermal accommodation, the height of potential barriers, and a porosity coefficient. The central example is a cyclic three-compartment system consisting of two thermal walls at different temperatures and a potential barrier. For full thermal accommodation we obtain closed-form expressions for the entropy production rate and net probability circulation around the cycle, revealing a thermal ratchet effect analogous to thermal transpiration.
