Istituto dei Sistemi Complessi-CNR and Dipartimento di Fisica, Università di Roma Sapienza, P. le Aldo Moro 2, 00185 Rome, Italy.
Phys Rev E. 2016 Apr;93:042116. doi: 10.1103/PhysRevE.93.042116. Epub 2016 Apr 14.
We investigate a kinetic heat engine model composed of particles enclosed in a box where one side acts as a thermostat and the opposite side is a piston exerting a given pressure. Pressure and temperature are varied in a cyclical protocol of period τ: their relative excursions, δ and ε, respectively, constitute the thermodynamic forces dragging the system out of equilibrium. The analysis of the entropy production of the system allows us to define the conjugated fluxes, which are proportional to the extracted work and the consumed heat. In the limit of small δ and ε the fluxes are linear in the forces through a τ-dependent Onsager matrix whose off-diagonal elements satisfy a reciprocal relation. The dynamics of the piston can be approximated, through a coarse-graining procedure, by a Klein-Kramers equation which-in the linear regime-yields analytic expressions for the Onsager coefficients and the entropy production. A study of the efficiency at maximum power shows that the Curzon-Ahlborn formula is always an upper limit which is approached at increasing values of the thermodynamic forces, i.e., outside of the linear regime. In all our analysis the adiabatic limit τ→∞ and the the small-force limit δ,ε→0 are not directly related.
我们研究了一个由封闭在盒子中的粒子组成的动力学热机模型，其中一侧充当恒温器，另一侧是施加给定压力的活塞。压力和温度以周期为 τ 的周期性协议变化：它们的相对偏移量 δ 和 ε 分别构成了将系统带出平衡的热力学力。对系统熵产生的分析允许我们定义共轭通量，它们与提取的功和消耗的热成正比。在 δ 和 ε 很小时，通量通过 τ 相关的 Onsager 矩阵在线性的力中是线性的，该矩阵的非对角元素满足互反关系。通过粗粒化过程，活塞的动力学可以近似为 Klein-Kramers 方程，该方程在线性区域内为 Onsager 系数和熵产生提供了解析表达式。最大功率效率的研究表明，Curzon-Ahlborn 公式始终是一个上限，随着热力学力的增加而接近，即在超出线性区域的情况下。在我们的所有分析中，绝热极限 τ→∞和小力极限 δ，ε→0 没有直接关系。
