Thermodynamics and emergent thermomechanical response of a quantum ring with nonminimal spin--orbit coupling

Abstract

We investigate the thermodynamic and emergent thermomechanical properties of fermions confined to a one-dimensional quantum ring with effective spin--orbit interactions induced by nonminimal couplings to antisymmetric tensor fields. Using the exact spectrum obtained in the companion work, we develop canonical and grand-canonical descriptions and show that the coupling parameter~$\xi$ deforms the angular-momentum branches, reorganizing the low-energy spectrum and leaving clear signatures in the internal energy, entropy, heat capacity, and spin--orbit response functions. We also formulate an effective thermomechanical description by treating the ring circumference as a quasi-static thermodynamic variable. This leads to a pressure-like quantity and associated response coefficients, directly linked to the microscopic spectrum. In the grand-canonical ensemble, Fermi statistics strongly enhance the response, producing coupling-dependent instabilities and sign changes reminiscent of mesoscopic de~Haas--van Alphen oscillations. Finally, we introduce a phenomenological interacting extension based on an exponential resummation of the free energy, showing that collective effects can sharpen the thermomechanical response and induce anomalous thermal contraction. Our results connect spectral deformation, finite-size thermodynamics, and emergent mechanical behavior in spin--orbit-active quantum rings.

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