Hierarchical Structure of Generalized Thermodynamic and Informational Entropy

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.Entropy 2018, 20, 553 2 of 19 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.

Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle

“…For a recent review of other principles, see also in [ 32 ]. For the discussion between entropy arising from information theory and thermodynamics, see in [ 33 ]. For the sake of simplicity, let us consider canonical ensemble, i.e., fluctuations in internal energy.…”

Hierarchical Information Entropy System Model for TWfMS

“…Furthermore, considering entropy as the main thread running through WfMS's physics and informatics characteristics [33], from the view of a dissipative structure system, this paper proposed a hierarchical information entropy system model for TWfMS. This means that the deterministic entropy of the WfMS is always in a non-equilibrium state, even the state of being far from equilibrium [58][59][60][61], and that the aim of the users is used to maintain it in such a stable non-equilibrium state with current requirements. Alternatively, it encounters a new stable non-equilibrium state from the previous non-equilibrium state, due to the unavoidable continuous requirement changes [62][63][64].…”

Chemical and Mechanical Aspect of Entropy-Exergy Relationship

“…The rationale to define chemical exergy is based on the confrontation of thermal and chemical aspect of cyclic processes. Usually, temperature is the intensive property determining the Carnot cycle representing the highest efficiency cyclic process and constituting the consequence of the non-existence of perpetual motion machine of the second kind (PMM2) [13]. However, if the same Carnot cycle is regarded as characterized by the chemi-cal potential as an intensive property, instead of temperature, then the Carnot chemical cycle constitutes the symmetric process of a Carnot thermal cycle, considering pressure as the common reference [13].…”

“…Usually, temperature is the intensive property determining the Carnot cycle representing the highest efficiency cyclic process and constituting the consequence of the non-existence of perpetual motion machine of the second kind (PMM2) [13]. However, if the same Carnot cycle is regarded as characterized by the chemi-cal potential as an intensive property, instead of temperature, then the Carnot chemical cycle constitutes the symmetric process of a Carnot thermal cycle, considering pressure as the common reference [13]. Hence, based on the chemical potential, a chemical machine model can be described in terms of a chemical conversion cyclic process as the homology of a thermal conversion cyclic process for which balances and efficiencies can be stated [11,12].…”

“…The above equation is similar to the already known canonical definition of physical exergy [14][15][16]; this expression is used to define the exergy that is identified by the superscript "C", standing for "Chemical", according to the definition reported in the literature [13] as pointed out above.…”