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arXiv:1309.1352

Between Being and Becoming: a meta-theoretical approach to irreversibility

Neri, Davide

Published Sep 5, 2013• 0 citations
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Abstract

The relationship between reversible-dynamical and irreversible-thermodynamic descriptions is analyzed from a meta-theoretical point of view. A network of inter-theoretical relations is drawn by means of asymptotic relations and complementarity. It is argued that the "paradox" between micro-reversibility and macro-irreversibility can be overcome by assuming a meta-complementarity relation existing between different levels of physical description, preserving a realist conception.

DOI
10.48550/arxiv.1309.1352

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The relationship between reversible-dynamical and irreversible-thermodynamic descriptions is analyzed from a meta-theoretical point of view. A network of inter-theoretical relations is drawn by means of asymptotic relations and complementarity. It is argued that the "paradox" between micro-reversibility and macro-irreversibility can be overcome by assuming a meta-complementarity relation existing between different levels of physical description, preserving a realist conception.
Abstract Quantum mechanics for describing the behavior of microscopic entities and thermodynamics for describing macroscopic systems exhibit separate time concepts. Whereas many theories of modern physics interpret processes as reversible, in thermodynamics, an expression for irreversibility and the so-called time arrow has been developed: the increase of entropy. The divergence between complete reversibility on the one hand and irreversibility on the other is called the paradox of time. Since more than hundred years many efforts have been devoted to unify the time concepts. So far, the efforts were not successful. In this paper a solution is proposed on the basis of matter-energy equivalence with an energetic distinction between matter and mass. By refraining from interpretations predominant in modern theoretical physics, the first and second laws of thermodynamics can be extended to fundamental laws of nature, which are also valid at quantum level.
In view of the fact that physical measurements represent transmission of information, a general definition based on the measure of lack of knowledge in information theory can be introduced for different entropies each of them corresponding to one particular kind of measurement. By means of this entropy concept the problem of the consistency of microscopic reversibility and maeroscopic irreversibility is studied. Under certain conditions it can be shown that the reversible microscopic equation of motion leads to the result that all entropies corresponding to reduced quantities, i.e., to quantities which do not determine the microscopic state of the system completely, can never decrease. However, it is to be noted that this behavior is symmetric in time, in the classical as well as in the quantum mechanical case. Irreversibility is so related on the one hand to incomplete description of a system, but on the other also to the fact that theoretical statements can be verified by experiments in the future only. The validity of the results obtained within the framework of ensemble theory for a single physical system is dtscussed. As applications of the general ideas a system of free particles and the Boltzmann gas are treated. (auth)
In view of the fact that physical measurements represent transmission of information, a general definition based on the measure of “lack of knowledge” in information theory can be introduced for different entropies each of them corresponding to one particular kind of measurement. By means of this entropy concept the problem of the consistency of microscopic reversibility and macroscopic irreversibility is studied. Under certain conditions it can be shown that the reversible microscopic equation of motion leads to the result that all entropies corresponding to “reduced” quantities, i.e. to quantities which do not determine the microscopic state of the system completely, can never decrease. However, it is to be noted that this behaviour is symmetric in time, in the classical as well as in the quantum mechanical case. Irreversibility is so related on the one hand to incomplete description of a system, but on the other also to the fact that theoretical statements can be verified by experiments in the future only. The validity of the results obtained within the framework of ensemble theory for a single physical system is discussed. As applications of the general ideas a system of free particles and the BOLTZMANN gas are treated.
We had previously shown [T. Yarman et al., Results Phys. 10 (2018) 818–821] that the classical adiabatic relation pV 5/3=Constant for an ideal monatomic gas admits a direct quantum-mechanical formulation in terms of Planck’s constant and confinement-dependent quantum-state indices. This result suggests that macroscopic thermodynamic scaling laws reflect an underlying quantum-state structure. In the present work, we revisit this quantum-state scaling framework and discuss how it may provide a complementary language for thermodynamic accessibility and macroscopic irreversibility. In particular, we emphasize the conceptual distinction between microscopic reversibility, the arrow of time, and operational macroscopic irreversibility. Within this perspective, irreversibility may be interpreted in terms of asymmetries in accessible quantum-state configurations under changing confinement and energy conditions, while the underlying microscopic equations remain formally time-reversal symmetric. At the same time, the concept of operationally inaccessible microscopic quantum reconstruction, such as that with regards to fission, naturally emerges. Still, we do not claim to replace Boltzmannian, correlation-based, or information-theoretic approaches. Rather, the present study proposes a complementary quantum-state scaling perspective for discussing thermodynamic accessibility and the macroscopic evolution of complex systems. Even so, within the present framework, these practical limitations on thermodynamic accessibility do not necessitate a breakdown of formal microscopic reversibility; rather, they align with the Boltzmannian view that macroscopic reversals remain formally possible yet are rendered overwhelmingly inaccessible in practice.