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Heat is a type of energy transfer that is caused by a temperature difference, and it can change the temperature of an object. Since heat is a form of energy, its SI unit is the joule (J). Another common unit of energy often used for heat is the calorie (cal), which is defined as the energy needed to change the temperature of 1 g of water by 1 °C, specifically between 14.5 °C and 15.5 °C, since the energy needed shows a slight temperature dependence. Another commonly used unit is...
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For a system that undergoes a thermodynamic process at a constant volume condition, the heat absorbed is used only to increase the system's internal energy and not for doing any kind of work. While for a system undergoing a thermodynamic process under a constant pressure condition, the amount of heat absorbed is used not only for increasing the internal energy (as a function of temperature) but also for doing some work. The molar heat capacity is the amount of heat required to increase the...
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Heat capacity is the ratio of heat absorbed by the substance corresponding to its temperature change. It is also called thermal capacity and the SI unit of heat capacity is J/K. Whereas, specific heat capacity is defined as the amount of heat necessary to change the temperature of 1 kg of a substance by 1 K and is also called massic heat capacity. Its SI unit is J/kg⋅K.
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The number of independent ways a gas molecule can move along straight line, rotate, and vibrate is called its degrees of freedom. Supposing d represents the number of degrees of freedom of an ideal gas, the molar heat capacity at constant volume of an ideal gas in terms of d is
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Characterization of Thermal Transport in One-dimensional Solid Materials
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Heat Diffusion Invariant.

Liujun Xu1, Pengfei Zhuang2, Fubao Yang1

  • 1Graduate School of China Academy of Engineering Physics, Beijing 100193, China.

Physical Review Letters
|August 27, 2025
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Summary

Researchers developed a heat diffusion invariant to classify thermal structures, enabling precise design of transient thermal metamaterials for applications in thermal management and metamaterial design.

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Area of Science:

  • Physics
  • Materials Science
  • Thermodynamics

Background:

  • Topological invariants are established for classifying geometric features in electronic, photonic, and phononic systems.
  • A unified invariant for classifying functional properties of thermal structures is currently lacking.

Purpose of the Study:

  • To formulate a novel heat diffusion invariant for thermal structures.
  • To establish a correlation between thermal functionality and diffusivity.
  • To enable the design of advanced thermal metamaterials.

Main Methods:

  • Formulation of a heat diffusion invariant.
  • Experimental verification using a freeform transient thermal cloak.
  • Exploration of applications in thermal convection and radiation.

Main Results:

  • The heat diffusion invariant explicitly correlates thermal functionality with diffusivity.
  • A unified framework for diverse thermal metamaterials is established.
  • The invariant facilitates the design of freeform transient thermal metamaterials with isotropic thermal conductivity.

Conclusions:

  • The heat diffusion invariant provides a new paradigm for designing thermal metamaterials.
  • This invariant is applicable to thermal cloaking, illusion, convection, and radiation.
  • The findings open new avenues for thermal management and nonequilibrium transport studies.