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High dynamic range novel view synthesis (HDR-NVS) reconstructs scenes with dynamic details by fusing multi-exposure low dynamic range (LDR) views, yet it struggles to capture ambient illumination-dependent appearance. Implicitly supervising HDR content by constraining tone-mapped results fails in correcting abnormal HDR values, and results in limited gradients for Gaussians in under/over-exposed regions. To this end, we introduce PhysHDR-GS, a physically inspired HDR-NVS framework that models scene appearance via intrinsic reflectance and adjustable ambient illumination. PhysHDR-GS employs a complementary image-exposure (IE) branch and Gaussian-illumination (GI) branch to faithfully reproduce standard camera observations and capture illumination-dependent appearance changes, respectively. During training, the proposed cross-branch HDR consistency loss provides explicit supervision for HDR content, while an illumination-guided gradient scaling strategy mitigates exposure-biased gradient starvation and reduces under-densified representations. Experimental results across realistic and synthetic datasets demonstrate our superiority in reconstructing HDR details (e.g., a PSNR gain of 2.04 dB over HDR-GS), while maintaining real-time rendering speed (up to 76 FPS). Code and models are available at this https URL.