介观统计热力学理论与实验

Theoretical and experiments of mesoscopic statistical thermodynamics

对于只有有限自由度的介观小系统,传统的热力学定律是否成立?温度、熵、做功、传热、等温过程、Carnot循环这些概念还是否有效?是否需要对原来适用于宏观系统的传统热力学理论进行修改或扩充、以适用于这样的小系统?在过去近20年里,我们深入研究了在介观小系统和量子系统中热力学基本概念的推广(例如什么是量子等温过程)以及基本热力学定律的适用性问题.研究表明,在系综平均意义上热力学定律仍然适用于小系统;考虑了Maxwell妖的信息擦除功耗后,热力学第二定律不会被违反;“小系统”的统计热力学具有一些新的特性,由于系统和环境之间的耦合不可忽略,有限系统的平衡态分布偏离正则系综,这可以描述诸如黑洞等小系统的辐射关联及其信息丢失现象;在任意远离平衡的情况下,热力学量的涨落变得十分显著,并且热力学量的分布函数满足一些严格成立的恒等式.这些恒等式定义了所谓的涨落定理,由此通过测量非平衡过程的物理量(如功分布)可以获得平衡过程的物理量相对值(如自由能差等).此外,尽管量子属性和信息论的考虑为统计热力学带来一些有别于经典和传统的特性,有助于理解Gibbs佯谬和Maxwell妖等基本问题,但需要指出的是,量子热机和信息辅助热机的效率并没有超越经典热机.随着在小系统中引入运动方程,热力学和力学之间的联系变得更加紧密,能够从第一性原理出发研究非平衡过程的能量耗散和热机的功率、效率优化及其最优调控微分几何化等问题.在对具体热循环过程熵产生问题的研究中,对得到的功率-效率约束关系进行了系统性的实验检验.

Does thermodynamics still hold true for mecroscopic small systems with only limited degrees of freedom?Do concepts such as temperature,entropy,work done,heat transfer,isothermal processes,and the Carnot cycle remain valid?Does the thermodynamic theory for small systems need modifying or supplementing compared with traditional thermodynamics applicable to macroscopic systems?Taking a single-particle system for example,we investigate the applicability of thermodynamic concepts and laws in small systems.We have found that thermodynamic laws still hold true in small systems at an ensemble-averaged level.After considering the information erasure of the Maxwell’s demon,the second law of thermodynamics is not violated.Additionally,‘small systems’bring some new features.Fluctuations in thermodynamic quantities become prominent.In any process far from equilibrium,the distribution functions of thermodynamic quantities satisfy certain rigorously established identities.These identities are known as fluctuation theorems.The second law of thermodynamics can be derived from them.Therefore,fluctuation theorems can be considered an upgradation to the second law of thermodynamics.They enable physicists to obtain equilibrium properties(e.g.free energy difference)by measuring physical quantities associated with non-equilibrium processes(e.g.work distributions).Furthermore,despite some distinct quantum features,the performance of quantum heat engine does not outperform that of classical heat engine.The introduction of motion equations into small system makes the relationship between thermodynamics and mechanics closer than before.Physicists can study energy dissipation in non-equilibrium process and optimize the power and efficiency of heat engine from the first principle.These findings enrich the content of thermodynamic theory and provide new ideas for establishing a general framework for non-equilibrium thermodynamics.