Thermal Spectra Without Detailed Balance
TLDR
This paper demonstrates that thermal spectra can arise from the emission kernel's structure, not necessarily from probe thermalization or detailed balance.
Key contributions
- Challenges the assumption that a thermal spectrum always signifies detailed balance or probe thermalization.
- Demonstrates that thermal spectra can emerge from the emission kernel's structure, even without probe thermalization.
- Identifies "thermally degenerate" emission kernels, like Thomson scattering, as a source of such spectra.
- Proposes a kernel-based criterion to differentiate genuine thermal equilibrium from kernel-induced thermal spectra.
Why it matters
This research redefines the interpretation of thermal spectra, showing they don't always indicate true thermal equilibrium. It offers a crucial new criterion for analyzing physical systems, particularly in contexts where probe thermalization is often assumed.
Original Abstract
A thermal spectrum is often taken as a signature that the emitted probe has reached detailed balance with the surrounding medium. We show that this interpretation is not generally valid by studying how the microscopic emission kernel determines the macroscopic spectrum. In $3+1$ dimensions, a simple thermal spectrum can be generated without probe thermalization when the relevant kernel belongs to a thermally degenerate class. A representative case is realized when the differential cross section depends on the scattering angle but carries no additional dependence on the Mandelstam variable $s$, as in low-energy Thomson scattering. Our results provide a kernel-based criterion for distinguishing genuine probe--medium exchange equilibrium from thermal spectra produced by the structure of the emission kernel itself.
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