In this paper, we present an application of the variational quantum simulation (VQS) framework to capture finite temperature open system dynamics on near-term quantum hardware. By embedding the generalized amplitude damping channel into the VQS algorithm, we model energy exchange with a thermal bath through its Lindblad representation and thereby simulate realistic dissipative effects. To explore a wide range of activation behaviors, we introduce a nonadditive relaxation time model using a generalized form of the Arrhenius law, based on the phenomenological parameter $q$. We compare our method on driven qubit systems subject to both static and composite time-dependent fields, comparing population evolution and trace distance errors against reference numerical solutions. Our results demonstrate that (1) VQS accurately maps the effective nonunitary generator under GAD, (2) smoother drive envelopes induced by nonaddtive parameters suppress high-frequency components and yield lower simulation errors, and (3) the variational manifold exhibits dynamical selectivity, maintaining mapping fidelity even as the reference numerical solution's sensitivity to $q$ increases.

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• Open quantum systems
• Quantum algorithms & computation
• Quantum simulation