Quantum Thermodynamics at Geometric and Physical Boundaries: From Thermal Casimir Stresses to Modular Horizon Entropy
Year: 2026
Type: preprint
Abstract: We formulate a unified relativistic framework for quantum thermodynamics at physical, causal, and entangling boundaries. In standard flat Minkowski space, the quantum vacuum represents an inert zero-entropy state. However, the introduction of a boundary restricts spectral modes, converting vacuum entanglement into explicit non-equilibrium thermodynamic observables. First, utilizing the imaginary-time Matsubara formulation for a scalar field on a bounded manifold, we derive the finite-temperature Casimir free energy and prove that boundary surface terms enforce the Nernst Heat Theorem (Third Law of Thermodynamics) as T -> 0. Second, we demonstrate that a uniformly accelerated observer’s causal Rindler horizon operates as a thermal boundary: tracing across the horizon transforms the pure vacuum into an exact Gibbs canonical state characterized by the Unruh temperature T_U = \hbar a / 2\pi c k_B. Third, employing quantum relative entropy across arbitrary entangling boundaries, we prove that the First Law of Thermodynamics (dS = dQ / T) is the exact macroscopic manifestation of the modular operator identity \Delta S_vN = \Delta . Finally, using the Brown-York quasi-local stress tensor on boundaries with non-zero extrinsic curvature, we derive the localized boundary pressure and recover the generalized Bekenstein-Hawking area entropy without heuristic assumptions.
Author: Hossain, A.S.M. Imam
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213758179
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