We analyze in the context of geometrothermodynamics a Legendre invariant metric structure in the equilibrium space of an ideal gas. We introduce the concept of thermodynamic geodesic as a succession of points, each corresponding to a state of equilibrium, so that the resulting curve represents a quasi-static process. A rigorous geometric structure is derived in which the thermodynamic geodesics at a given point split the equilibrium space into two disconnected regions separated by adiabatic geodesics. This resembles the causal structure of special relativity, which we use to introduce the concept of adiabatic cone for thermodynamic systems. This result might be interpreted as an alternative indication of the inter-relationship between relativistic physics and classical thermodynamics.
Thermodynamic Cost for Classical Counterdiabatic Driving
最近越来越多的兴趣的热力学成本的捷径绝热（STA）的动机，我们考虑的成本驱动一个经典系统的所谓的反绝热驱动（CD）。要做到这一点，我们进行了三个步骤：首先，我们回顾了最近在文献中提出的一般定义的热力学成本驱动的哈密顿系统;然后，我们提供了一个新的补充定义的成本，这是特别相关的情况下，平均超额工作消失;最后，我们将我们的一般框架的情况下，CD。有趣的是，我们发现在这种情况下，我们的结果与Funo et al. PRL，118（10）：100602，2017中报道的结果完全相同。特别是，我们表明，CD的速度和成本之间的普遍权衡也存在于经典的情况下。为了说明我们的观点，我们考虑的例子，含时谐振子的绝热控制的不同策略。
