Fundamentally, any phase transition in a material between states of different degrees of order and disorder (entropy) can be used to pump heat. Most refrigeration systems are based upon a liquid/gas phase transition, but the alignment of domains in a material due to magnetism will do the job as well. Magnetic refrigeration has been used for almost a century to achieve very low (less than 1° K) temperatures, and recent research has suggested magnetic refrigeration may be able to replace conventional compressor-based systems by a solid state solution with no moving parts.
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Another solid state heat pump technology is the Peltier effect. Think of it as applying power to a thermocouple, with heat sinks. Common in industrial applications already:
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