Thermal Wavelength

The Thermal Wavelength is the matter-wave length scale set by a particle's mass and temperature, used in BPT as the yardstick for the boundary between quantum coherence and classical behavior. It shrinks as mass and temperature rise. The book compares it with the phase correlation length of a substrate system: when the phase correlation length is shorter than the thermal wavelength, ξ⟢ < λΘ, the system is in the classical regime. With the Mass-Dependent Coherence Time, which falls as the cube root of mass, it makes up the book's framework for the quantum-classical transition and for testable signatures of binary substrate architecture. The formal statement is λΘ = h/√(2πmk_BT), where λΘ is the Thermal Wavelength, h the Planck constant, m the particle mass, k_B the Boltzmann constant and T the temperature; ξ⟢ is the phase correlation length it is compared with. Dimensions from the book's Where-list: λΘ [𝕃], m [𝕄], k_B [𝕄·𝕃²·𝕋⁻²·Θ⁻¹], T [Θ], ξ⟢ [𝕃], π [∅]. It connects to the Quantum-Classical Criterion, Mass-Dependent Coherence Time, Coherence Factor and Decoherence Transition.