Measurable Consequences of the Local Breakdown of the Concept of Temperature

Abstract

Local temperature defined by a local canonical state of the respective subsystem, does not always exist in quantum many body systems. Here, we give some examples of how this breakdown of the temperature concept on small length scales might be observed in experiments: Measurements of magnetic properties of an anti-ferromagnetic spin-1 chain. We show that those magnetic properties are in fact strictly local. As a consequence their measurement reveals whether the local (reduced) state can be thermal. If it is, a temperature may be associated to the measurement results, while this would lead to inconsistencies otherwise.

arXiv commentsome comments added, results remain unchanged

References in corpus (8)

• Entangled Rings
• Existence of temperature on the nanoscale
• On testing the violation of the Clausius inequality in nanoscale electric circuits
• Entanglement Energetics at Zero Temperature
• Gaussian quantum fluctuations in interacting many particle systems
• Multi-particle States in Spin-1 Chain System CsNiCl3
• Local Versus Global Thermal States: Correlations and the Existence of Local Temperatures
• Coupling theory for counterion distributions based in Tsallis statistics

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• Nano-Thermodynamics: On the minimal length scale for the existence of temperature
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