论文标题
在热水浴中运行的系统的熵生产率的确切时间依赖性分析解决方案，其温度在太空中线性变化
Exact time-dependent analytical solutions for entropy production rate for a system that operates in a heat bath where its temperature varies linearly in space
论文作者
论文摘要
通过获得精确的时间依赖性溶液来研究布朗电动机的非平衡热力学特征。反过来，这使我们不仅可以研究长时间的属性（稳态），还可以研究系统的行为。自由能，熵产生的一般表达$ {\ dot e} _ {p}（t）$以及熵提取$ {\ dot h} _ {d}（t）$率是为一个由时间独立依赖性力和依从性的varmal vy vary vary vary vary vary vary vary vary vermant驱动的系统。我们表明，对于在冷藏库之间运行的系统，大多数热力学数量在长期限制中接近非平衡稳态。在稳定状态下，自由能的变化变得最小。但是，对于在温度在空间上线性变化的热浴中运行的系统，熵的产生和提取速率接近非平衡稳态，而自由能的变化在太空中线性变化。这表明，与在平衡处的系统不同，当系统从平衡中驱动时，它们的自由能可能不会最小化。进一步比较了在热水和冷浴之间运行的系统的热力学特性，并与在热浴中运行的系统进行对比，该系统的温度与反应坐标一起在太空中线性变化。我们表明，线性变化的温度案例的熵，熵产生和提取率要比在热浴之间进行操作的系统要大得多，该系统揭示了这种系统本质上是不可逆的。在这两种情况下，在存在负载或保留明显的温度差时，熵$ s（t）$单调随时间和饱和为恒定值，$ t $ a $ t $ a $ t $进一步加强。
The nonequilibrium thermodynamics feature of a Brownian motor is investigated by obtaining exact time-dependent solutions. This in turn enables us to investigate not only the long time property (steady-state) but also the short time the behavior of the system. The general expressions for the free energy, entropy production ${\dot e}_{p}(t)$ as well as entropy extraction ${\dot h}_{d}(t)$ rates are derived for a system that is genuinely driven out of equilibrium by time-independent force as well as by spatially varying thermal background. We show that for a system that operates between hot and cold reservoirs, most of the thermodynamics quantities approach a non-equilibrium steady state in the long time limit. The change in free energy becomes minimal at a steady state. However for a system that operates in a heat bath where its temperature varies linearly in space, the entropy production and extraction rates approach a non-equilibrium steady state while the change in free energy varies linearly in space. This reveals that unlike systems at equilibrium, when systems are driven out of equilibrium, their free energy may not be minimized. The thermodynamic properties of a system that operates between the hot and cold baths are further compared and contrasted with a system that operates in a heat bath where its temperature varies linearly in space along with the reaction coordinate. We show that the entropy, entropy production, and extraction rates are considerably larger for linearly varying temperature case than a system that operates between the hot and cold baths revealing such systems are inherently irreversible. For both cases, in the presence of load or when a distinct temperature difference is retained, the entropy $S(t)$ monotonously increases with time and saturates to a constant value as $t$ further steps up.
