Environment
Environment packages a macroscopic bath as a record of degrees-of-freedom count, positive temperature, and coupling strength. Quantum decoherence calculations in Recognition Science cite this record when constructing pointer-state selection from J-cost minima. The declaration is a plain structure definition carrying one positivity constraint.
claimAn environment is a triple $(N, T, g)$ where $N$ is a natural number of degrees of freedom, $T > 0$ is temperature, and $g$ is interaction strength.
background
The module QF-003 derives pointer states as the stable configurations that minimize J-cost under environmental coupling. Pointer states correspond to neutral windows in the J-cost landscape; superpositions acquire high J-cost through entanglement and are suppressed. Upstream, the actualization operator A maps a configuration to the J-minimizing outcome, while temperature is recovered as the inverse Lagrange multiplier from the Boltzmann distribution.
proof idea
This is a structure definition that directly assembles the three parameters together with the temperature positivity field.
why it matters in Recognition Science
The record supplies the environment model required by einselection_from_jcost and decoherenceTime. It fills the QF-003 target of obtaining classical pointer states from neutral windows in the J-cost landscape. The same structure appears in the continuous quantum-to-classical crossover that depends on system size, temperature, and coupling.
scope and limits
- Does not encode the explicit J-cost functional.
- Does not restrict interactions to a particular Lindblad form.
- Does not compute numerical decoherence timescales.
formal statement (Lean)
56structure Environment where
57 degrees_of_freedom : ℕ
58 temperature : ℝ
59 interaction_strength : ℝ
60 temp_pos : temperature > 0
61
62/-- A typical macroscopic environment (room temperature, many particles). -/