We suggest a new geometrical interpretation of the renormalization-group transformation near the critical point. Using the Weinhold-Ruppeiner metricization, conformal Killing symmetry is assumed and scaling laws are verified.

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Metricization of thermodynamic-state space and the renormalization group | Synapse

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Diósi et al. (Fri,) studied this question.

synapsesocial.com/papers/6a1ff6433224f8dacd0db034 https://doi.org/https://doi.org/10.1103/physreva.29.3343

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1Thermodynamics: A Riemannian geometric model1979 · 742 citations
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Thermodynamics: A Riemannian geometric model1979 · 742 citations
2Introduction to Phase Transitions and Critical Phenomena1972 · 4,116 citations
3Metric geometry of equilibrium thermodynamics1975 · 752 citations
4Far infrared spectra of van der Waals molecules in HCl–noble gas mixtures1980 · 26 citations
5Statistical distance and Hilbert space1981 · 794 citations