发表机构
Department of Physics, İstanbul University（伊斯坦布尔大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过量纲约化将热力学第一定律转化为开放系统的显式运动方程，证明其与受驱动阻尼谐振子和RLC电路动力学等价，并构建了统一的拉格朗日表述。
AI 中文摘要
热力学系统内能的变化从根本上由热力学第一定律描述。然而，第一定律具有高度紧凑的形式，并未明确揭示系统的动力学，也未提供相应的运动方程。虽然力学和电学系统可以显式写出运动方程，但据我们所知，对于热力学系统，类似的动力学表述尚未直接从第一定律建立。在本工作中，我们证明，通过量纲约化，第一定律可以从其紧凑的热力学形式转化为开放热力学系统的显式运动方程。值得注意的是，所得方程揭示出，该热力学系统的动力学等价于受驱动的阻尼谐振子和受驱动的RLC电路。对所得方程和有效系数的详细量纲分析证明了所得表述的内部一致性。我们进一步对力学、电学和热力学系统进行了系统比较，并表明，尽管它们的物理起源不同，它们共享相同的普适动力学结构。最后，我们构建了热力学系统的拉格朗日表述，并确立了其与力学和电学系统的拉格朗日描述之间的对应关系。这些结果表明，显式运动方程可以直接从热力学第一定律生成，并揭示了热力学、力学和电学系统背后的共同动力学框架。
英文摘要
Changes in the internal energy of a thermodynamic system are fundamentally described by the first law of thermodynamics. However, the first law has a highly compact form that does not explicitly reveal the dynamics of the system or provide a corresponding equation of motion. While equations of motion can be written explicitly for mechanical and electrical systems, an analogous dynamical formulation for thermodynamic systems has, to our knowledge, not been established directly from the first law. In this work, we show that, through dimensional reduction, the first law can be transformed from its compact thermodynamic form into an explicit equation of motion for an open thermodynamic system. Remarkably, the resulting equation has the same mathematical structure as the equations governing a driven damped harmonic oscillator and a driven series RLC circuit. Detailed dimensional analyses of the derived equation and the effective coefficients further confirm the dimensional consistency of the formulation. We further perform a systematic comparison of the mechanical, electrical, and thermodynamic systems and show that, despite their distinct physical origins, they share the same universal dynamical structure. Finally, we construct a Lagrangian formulation of the thermodynamic system and establish its correspondence with the Lagrangian descriptions of the mechanical and electrical systems. These results demonstrate that an explicit equation of motion can be generated directly from the first law of thermodynamics and reveal a common dynamical framework underlying thermodynamic, mechanical, and electrical systems.
CommentsRevised version with minor corrections and clarifications
