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Article

Hierarchical Structure of Generalized Thermodynamic and Informational Entropy

Department of Astronautical, Electrical and Energy Engineering (DIAEE), Sapienza Università di Roma, 00184 Roma, Italy
Entropy 2018, 20(8), 553; https://doi.org/10.3390/e20080553
Received: 26 June 2018 / Revised: 23 July 2018 / Accepted: 23 July 2018 / Published: 25 July 2018
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
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 Second Law, 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 Second Law, the non-equipartition theorem of entropy is enunciated, which would be complementary to the equipartition theorem of energy derived from the First Law. View Full-Text
Keywords: hierarchical configuration; hierarchical structure; equilibrium; nonequilibrium; first law; second law; generalized thermodynamic entropy; generalized informational entropy; generalized exergy; equipartition theorem of energy; non-equipartition theorem of entropy hierarchical configuration; hierarchical structure; equilibrium; nonequilibrium; first law; second law; generalized thermodynamic entropy; generalized informational entropy; generalized exergy; equipartition theorem of energy; non-equipartition theorem of entropy
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MDPI and ACS Style

Palazzo, P. Hierarchical Structure of Generalized Thermodynamic and Informational Entropy. Entropy 2018, 20, 553. https://doi.org/10.3390/e20080553

AMA Style

Palazzo P. Hierarchical Structure of Generalized Thermodynamic and Informational Entropy. Entropy. 2018; 20(8):553. https://doi.org/10.3390/e20080553

Chicago/Turabian Style

Palazzo, Pierfrancesco. 2018. "Hierarchical Structure of Generalized Thermodynamic and Informational Entropy" Entropy 20, no. 8: 553. https://doi.org/10.3390/e20080553

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