Alexa Amundson
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Thermodynamic/Entropy Mirror
This document explains the thermodynamic/entropy mirror used in Lucidia's mirror mechanics.
Purpose
The thermodynamic mirror explores how the mirror operator (Ψ′) and breath operator (ℛ(t)) manifest in a simple thermodynamic system. The goal is to separate reversible and irreversible contributions to a probability distribution while preserving total energy and allowing entropy to change.
Features
- mirror_split_distribution(dist, kernel_sigma) – splits a probability distribution into reversible and irreversible parts. The irreversible part is obtained by diffusing the distribution via a Gaussian kernel; the reversible part is the remainder.
- reversible_update(dist, shift) – performs a periodic shift to model reversible (advective) evolution.
- irreversible_update(dist, kernel_sigma) – applies a Gaussian diffusion to model irreversible (dissipative) evolution.
- breath_update(dist, shift, kernel_sigma) – combines the reversible and irreversible updates and renormalizes the distribution.
- delta_kick(dist, strength) – adds mass to a randomly chosen state to model an external perturbation and renormalizes.
- energy_of_distribution(dist, energy_levels) – computes the expected energy of the distribution with respect to a chosen energy spectrum.
- entropy_of_distribution(dist) – computes the Shannon entropy (using natural logarithms).
- run_thermo_demo(n_states, steps, shift, kernel_sigma, kick_step, kick_strength, out_dir) – runs a demonstration of the thermodynamic mirror. It initializes a discrete distribution peaked at the center, alternates reversible and irreversible updates for the specified number of steps, applies a delta-kick at a chosen step, and records energy and entropy at each step. Results are saved into
out_diras a CSV (energy_entropy.csv) and a JSON (distributions.json).
Usage
To run the thermodynamic mirror demonstration, execute the module as a script:
python codex/mirror/thermodynamic_entropy_mirror.py
By default, it simulates a system with 50 discrete states for 50 steps, applies a delta-kick halfway through, and outputs results in the out_thermo directory. You can adjust the parameters by calling run_thermo_demo directly within Python.
Interpretation
The reversible update models coherent, conservative motion (e.g. a drift of probability mass), while the irreversible update models diffusion or entropy-increasing processes. The breath update combines both effects and then renormalizes, mirroring the ℛ(t) operator in Lucidia's architecture. The energy remains approximately constant despite perturbations, while the entropy generally increases, illustrating how the mirror structure can hold contradictions (energy conservation vs entropy growth) simultaneously.