Abstract
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.
Highlights
Informational entropy is in turn an inherent property of matter as any physical state is characterized by an amount of information and a corresponding amount of uncertainty that depends on the scale of the system up to quantum where Heisenberg indetermination principle constitutes a physical fundamental
As entropy requires the concept of exergy, in turn derived from the available energy of the composite system-reservoir, the formulation of chemical exergy and mechanical exergy, in addition to thermal exergy, is needed to achieve the chemical entropy and mechanical entropy, in addition to thermal entropy, as components of the generalized thermodynamic entropy property, which enables demonstrating the necessity and sufficiency of stable equilibrium for equality of temperature, potential and pressure, proving the Second Law with a complete and consistent logical rationale
This irreversibility, related to the Second Law, is the essence of the non-equipartition theorem of entropy which would be complementary to the equipartition theorem of energy derived from the First Law
Summary
The title of the present article addresses both 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 treatise is here focused on physical aspects as a prerequisite to extend the conceptual framework to information science to pursue the attempt of achieving an overarching and unitary theory. The term “generalized thermodynamic entropy” addresses the physical aspect of phenomena occurring in any system. Entropy 2018, 20, 553 and its hierarchical structure associated to multi-scale system configuration; and (ii) the possibility (and, for a rigorous approach, the need) of extending to information science the generalization of foundations and properties in the thermodynamic domain with the aim of achieving a complete and consistent conceptual framework. The intent is here to highlight correlations among different facets of the theoretical and methodological building under elaboration by the community of physicists and information scientists
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