PNMS Case Study — Boltzmann Relaxation: Thermal Contact and Equilibrium in Signature Space
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| Format: | Recurso digital |
| Sprache: | Englisch |
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2026
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| _version_ | 1866901126603866112 |
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| author | Lami, Faical |
| author_facet | Lami, Faical |
| contents | <p><strong>Case study applying the Property-Neutral Matrixscope (PNMS) projection to thermal contact between two systems with heat capacities C_A and C_B. Two thermal states Σ_A and Σ_B located on the Boltzmann diagonal are used as input. The physical model of thermal contact produces an equilibrium temperature</strong></p> <p><strong>T_eq = (C_A·T_A + C_B·T_B) / (C_A + C_B)</strong></p> <p><strong>which conserves energy. The resulting state Σ_out is obtained by projecting the equilibrium quantities through Φ_R. The study compares the physical equilibrium temperature with the geometric midpoint of the two signatures, which corresponds to the geometric mean temperature √(T_A·T_B) under the logarithmic metric used in signature space. Signature distances are computed between the initial states and the equilibrium state, showing that the equilibrium point is generally displaced from the signature midpoint and that the displacement reflects entropy production and heat-capacity asymmetry. The analysis demonstrates how thermodynamic relaxation appears as a measurable structural movement of states along the statistical-mechanics diagonal in PNMS signature space. </strong></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18916514 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | PNMS Case Study — Boltzmann Relaxation: Thermal Contact and Equilibrium in Signature Space Lami, Faical entropy production heat capacity thermal equilibrium Boltzmann relation statistical mechanics thermodynamic systems signature space Planck normalization Boltzmann constant thermal contact <p><strong>Case study applying the Property-Neutral Matrixscope (PNMS) projection to thermal contact between two systems with heat capacities C_A and C_B. Two thermal states Σ_A and Σ_B located on the Boltzmann diagonal are used as input. The physical model of thermal contact produces an equilibrium temperature</strong></p> <p><strong>T_eq = (C_A·T_A + C_B·T_B) / (C_A + C_B)</strong></p> <p><strong>which conserves energy. The resulting state Σ_out is obtained by projecting the equilibrium quantities through Φ_R. The study compares the physical equilibrium temperature with the geometric midpoint of the two signatures, which corresponds to the geometric mean temperature √(T_A·T_B) under the logarithmic metric used in signature space. Signature distances are computed between the initial states and the equilibrium state, showing that the equilibrium point is generally displaced from the signature midpoint and that the displacement reflects entropy production and heat-capacity asymmetry. The analysis demonstrates how thermodynamic relaxation appears as a measurable structural movement of states along the statistical-mechanics diagonal in PNMS signature space. </strong></p> |
| title | PNMS Case Study — Boltzmann Relaxation: Thermal Contact and Equilibrium in Signature Space |
| topic | entropy production heat capacity thermal equilibrium Boltzmann relation statistical mechanics thermodynamic systems signature space Planck normalization Boltzmann constant thermal contact |
| url | https://doi.org/10.5281/zenodo.18916514 |