Palazzo Pierfrancesco
Department of Astronautical, Electrical and Energy Engineering (DIAEE), Sapienza Università di Roma, 00184 Roma, Italy.
Entropy (Basel). 2018 Jul 25;20(8):553. doi: 10.3390/e20080553.
The present research aimed at discussing the thermodynamic and informational aspects of entropy concept to propose a unitary perspective of its definitions as an inherent property of any system in any state. The dualism and the relation between physical nature of information and the informational content of physical states of matter and phenomena play a fundamental role in the description of multi-scale systems characterized by hierarchical configurations. A method is proposed to generalize thermodynamic and informational entropy property and characterize the hierarchical structure of its canonical definition at macroscopic and microscopic levels of a system described in the domain of classical and quantum physics. The conceptual schema is based on dualisms and symmetries inherent to the geometric and kinematic configurations and interactions occurring in many-particle and few-particle thermodynamic systems. The hierarchical configuration of particles and sub-particles, representing the constitutive elements of physical systems, breaks down into levels characterized by particle masses subdivision, implying positions and velocities degrees of freedom multiplication. This hierarchy accommodates the allocation of phenomena and processes from higher to lower levels in the respect of the equipartition theorem of energy. However, the opposite and reversible process, from lower to higher level, is impossible by virtue of the , expressed as impossibility of Perpetual Motion Machine of the Second Kind (PMM2) remaining valid at all hierarchical levels, and the non-existence of Maxwell's demon. Based on the generalized definition of entropy property, the hierarchical structure of entropy contribution and production balance, determined by degrees of freedom and constraints of systems configuration, is established. Moreover, as a consequence of the , the non-equipartition theorem of entropy is enunciated, which would be complementary to the equipartition theorem of energy derived from the .
本研究旨在探讨熵概念的热力学和信息学方面，以提出一种统一的观点，将其定义为任何状态下任何系统的固有属性。信息的物理本质与物质和现象物理状态的信息内容之间的二元性及其关系，在描述具有层次结构的多尺度系统中起着基础性作用。本文提出了一种方法，用于概括热力学和信息熵的性质，并在经典和量子物理领域描述的系统的宏观和微观层面上，刻画其规范定义的层次结构。该概念框架基于多粒子和少粒子热力学系统中几何和运动学构型及相互作用所固有的二元性和对称性。代表物理系统组成要素的粒子和亚粒子的层次结构，分解为以粒子质量细分表征的层次，这意味着位置和速度自由度的增加。这种层次结构根据能量均分定理，实现了现象和过程从较高层次到较低层次的分配。然而，由于第二类永动机（PMM2）在所有层次上都不可能存在，以及麦克斯韦妖不存在，从较低层次到较高层次的相反且可逆的过程是不可能的。基于熵性质的广义定义，建立了由系统构型的自由度和约束决定的熵贡献和产生平衡的层次结构。此外，作为[前文提及内容]的结果，阐述了熵的非均分定理，它将补充从[前文提及内容]导出的能量均分定理。
