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<p>We present a study of the thermal susceptibility associated with the Guyer-Krumhansl (GK) equation. This model is analyzed within the framework of causal linear response theory, which enables a causal and non-local description of thermal transport. We demonstrate that the real and imaginary parts of GK’s thermal susceptibility satisfy the Kramers-Krönig relations. Notably, unlike electromagnetic and mechanical systems where dissipation is linked to the imaginary part, in this case, thermal energy dissipation is associated with the real part of the susceptibility. Finally, we establish the sum rules for thermal susceptibility, which impose constraints on the value of Cattaneo’s response time.</p>

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Revisiting the Guyer-Krumhansl equation within the framework of causal linear response theory

  • 期刊论文

  • 发表日期：

    2025年7月26日

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  • Angela Camacho de la Rosa,
  • Rolando Pérez-Álvarez

摘要

We present a study of the thermal susceptibility associated with the Guyer-Krumhansl (GK) equation. This model is analyzed within the framework of causal linear response theory, which enables a causal and non-local description of thermal transport. We demonstrate that the real and imaginary parts of GK’s thermal susceptibility satisfy the Kramers-Krönig relations. Notably, unlike electromagnetic and mechanical systems where dissipation is linked to the imaginary part, in this case, thermal energy dissipation is associated with the real part of the susceptibility. Finally, we establish the sum rules for thermal susceptibility, which impose constraints on the value of Cattaneo’s response time.