Symbolic Thermodynamics: Entropy, Yield, Irreversibility, and Time
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2025
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| _version_ | 1866902184635924480 |
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| author | Naqvi, Ammar |
| author_facet | Naqvi, Ammar |
| contents | <p><em>This preprint develops a symbolic formulation of thermodynamics, grounded in the mathematically rigorous symbolic transformation framework detailed in <a href="https://doi.org/10.5281/zenodo.15238768" rel="noopener">Arithmorphics I</a> and <a href="https://doi.org/10.5281/zenodo.15238851" rel="noopener">Arithmorphics II</a>. It forms part of an ongoing series exploring the foundations and dynamics of symbolic systems based on admissible transformations. The first paper in the series is <a href="https://doi.org/10.5281/zenodo.15323722" rel="noopener">Symbolic Mechanics</a>. Constructive comments are welcome.</em></p> <p>We introduce a rigorous framework for <em>symbolic thermodynamics</em>, a transformation-based theory of entropy, temperature, and irreversibility derived entirely from discrete symbolic dynamics. Unlike classical thermodynamics, which relies on smooth differential structures and probabilistic ensembles, symbolic thermodynamics replaces continuity with computable, modular evolution rules defined over configuration spaces such as Z_n and Σ*. Building on the principles of <em>Symbolic Mechanics</em>, we define symbolic entropy through valuation-theoretic measures, derive its monotonicity under descent, and establish invariance and conservation laws applicable to all admissible symbolic observers. We formulate and prove a symbolic analogue of the Second Law of thermodynamics, showing that entropy increases strictly under irreversible symbolic evolution and that cyclic recurrence is structurally forbidden. The symbolic analogue of the First Law is expressed as a modular energy–entropy–work relation, grounded in transformation structure rather than heat or probability. We prove the <em>Symbolic Entropy Index Invariance Law</em> and the <em>Modular Entropy–Information Conservation Law</em>, demonstrating that symbolic entropy is both frame-invariant and recoverable from computable structural dynamics. Simulation case studies, including reversible automata, modular bifurcations, and symbolic decay, illustrate entropy growth, equilibrium, and observer-relative irreversibility. <em>Symbolic Thermodynamics</em> provides falsifiable predictions that diverge from classical theory, especially in domains such as cellular automata, quantum decoherence, and cosmological entropy asymmetry. As a computable, discrete, and algebraically grounded theory, symbolic thermodynamics offers a principled alternative to continuum-based models of physical evolution.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15442097 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Symbolic Thermodynamics: Entropy, Yield, Irreversibility, and Time Naqvi, Ammar Symbolic Thermodynamics Entropy Irreversibility Descent Dynamics Modular Systems Computable Physics Symbolic Mechanics Arithmorphics Time <p><em>This preprint develops a symbolic formulation of thermodynamics, grounded in the mathematically rigorous symbolic transformation framework detailed in <a href="https://doi.org/10.5281/zenodo.15238768" rel="noopener">Arithmorphics I</a> and <a href="https://doi.org/10.5281/zenodo.15238851" rel="noopener">Arithmorphics II</a>. It forms part of an ongoing series exploring the foundations and dynamics of symbolic systems based on admissible transformations. The first paper in the series is <a href="https://doi.org/10.5281/zenodo.15323722" rel="noopener">Symbolic Mechanics</a>. Constructive comments are welcome.</em></p> <p>We introduce a rigorous framework for <em>symbolic thermodynamics</em>, a transformation-based theory of entropy, temperature, and irreversibility derived entirely from discrete symbolic dynamics. Unlike classical thermodynamics, which relies on smooth differential structures and probabilistic ensembles, symbolic thermodynamics replaces continuity with computable, modular evolution rules defined over configuration spaces such as Z_n and Σ*. Building on the principles of <em>Symbolic Mechanics</em>, we define symbolic entropy through valuation-theoretic measures, derive its monotonicity under descent, and establish invariance and conservation laws applicable to all admissible symbolic observers. We formulate and prove a symbolic analogue of the Second Law of thermodynamics, showing that entropy increases strictly under irreversible symbolic evolution and that cyclic recurrence is structurally forbidden. The symbolic analogue of the First Law is expressed as a modular energy–entropy–work relation, grounded in transformation structure rather than heat or probability. We prove the <em>Symbolic Entropy Index Invariance Law</em> and the <em>Modular Entropy–Information Conservation Law</em>, demonstrating that symbolic entropy is both frame-invariant and recoverable from computable structural dynamics. Simulation case studies, including reversible automata, modular bifurcations, and symbolic decay, illustrate entropy growth, equilibrium, and observer-relative irreversibility. <em>Symbolic Thermodynamics</em> provides falsifiable predictions that diverge from classical theory, especially in domains such as cellular automata, quantum decoherence, and cosmological entropy asymmetry. As a computable, discrete, and algebraically grounded theory, symbolic thermodynamics offers a principled alternative to continuum-based models of physical evolution.</p> |
| title | Symbolic Thermodynamics: Entropy, Yield, Irreversibility, and Time |
| topic | Symbolic Thermodynamics Entropy Irreversibility Descent Dynamics Modular Systems Computable Physics Symbolic Mechanics Arithmorphics Time |
| url | https://doi.org/10.5281/zenodo.15442097 |