Abstract
We develop a unified, single-scale description of thermodynamics and quantum oscillations in electronic systems with a uniform areal density of screw dislocations under a uniform magnetic field. A single tunable gap, ℏ|ω_eff| with ω_eff=ω_c+ω_cl, organizes all equilibrium observables obtained from a compact harmonic-oscillator partition function: free energy, internal energy, entropy, heat capacity, magnetization, magnetic susceptibility, and magnetocaloric responses collapse onto universal hyperbolic kernels in x=ℏ|ω_eff|/(2k_BT). We identify a compensated-field regime where the transverse gap closes and the heat capacity reaches an equipartition plateau, providing a sharp signature of magnetoelastic interference. In transport and torque, the same scale rigidly shifts the Hall fan and compresses the 1/B period of de Haas-van Alphen and Shubnikov-de Haas oscillations when expressed in 1/B_eff, enabling a phase-unwarping protocol that metrologizes the dislocation density from a single field sweep. In mesoscopic samples, boundary corrections to the Landau degeneracy generate finite-size calorimetric oscillations that diagnose the effective magnetic length. Moderate disorder and weak interactions preserve the kernel structure while smoothing amplitudes. We outline an experimental roadmap combining on-chip calorimetry, torque magnetometry, and transport, and discuss device-level opportunities in caloritronics and strain engineering, magnetocaloric microcooling, magnetoelastic heat switching, and dilatometric transduction, where the single scale ℏ|ω_eff| enables rational design and optimization.