Decentralized Cryptocurrency Markets: The Time Crystal Concept in Atomic Clocks.

# Decentralized Cryptocurrency Markets: The Time Crystal Concept in Atomic Clocks. Let N be the network of Automated Market Makers (AMMs). Let P be the network of entangled econophysics particles. *During each "**tic**", the entangled econophysics **particles group** that compose **the quantum web rearrange their geopositioning**, causing a **transfer of energy between the AMMs**.* This can be expressed as follows: ``` ΔE = ∑(Vi - Vavg) * ΔMi ``` where ΔE is the change in energy, Vi is the value of Metatoken i, Vavg is the average value of all Metatokens in N, ΔMi is the change in the supply of Metatoken i during the "tic". The entangled econophysics particles monitor the state of the AMMs and make adjustments as necessary to ensure that they remain in balance. This can be expressed as follows: ``` ∂N/∂t = ∑(ΔVi/Δt) * Pi ``` Where ∂N/∂t is the rate of change of N over time, ΔVi/Δt is the rate of change of the value of Metatoken i over time, and Pi is the entangled econophysics particle that is associated with Metatoken i. Overall, this quantum mechanism uses the entangled econophysics particles to monitor and regulate the energy flow between the AMMs to maintain the equilibrium of the Metatoken market. # Extension to potential role of quantum gravity within a quantum web Let S be the sphere that represents the overall structure of the Metatoken market, centered around the singularity of a black hole. The sphere has a radius R and a surface area A. *The entangled econophysics particles are arranged in such a way that they form a kind of "**quantum web**" around the AMMs, which are located **at the edges of the system outside the "black hole"**.* The number of entangled particles in the web can be represented as follows: ``` N = (A/4) * (R/γ)² ``` where N is the number of entangled particles, γ is the gravitational constant, and A/4πR² is the surface density of the sphere. The Bekenstein bound states that the maximum amount of information that can be contained within a sphere is proportional to its surface area. Therefore, the maximum amount of information that can be contained within the Metatoken market sphere is: ``` I = (A/4) * ln(2) ``` where ln(2) represents the natural logarithm of 2. *The entangled econophysics particles act as a kind of "**quantum glue**" that holds the AMMs in **equilibrium**. The particles are constantly **monitoring** the state of the AMMs and making adjustments as necessary to ensure that they **remain in balance**.* This can be expressed as follows: ``` ∆S = (4/3)πR³ * ∆ρ ``` where ∆S is the change in the surface area of the sphere, ∆ρ is the change in the density of the sphere, and (4/3)πR³ represents the volume of the sphere. *The total **diversity** of the Metatoken market can be described using Shannon diversity index, which takes into account the number of different types of Metatokens and their **relative abundance**. The Shannon diversity index is given by:* ``` H = - ∑(pi * log2(pi)) ``` where pi is the relative abundance of Metatoken i. The total entropy of the Metatoken market can also be calculated using the Shannon entropy formula, which is: ``` S = - k * ∑(pi * log2(pi)) ``` where k is the Boltzmann constant. Overall, the decentralized logic of the black hole Metatoken market is maintained by the entangled econophysics particles at the edges of the system, and the total diversity and entropy of the market can be described using Shannon diversity index and entropy formulas. *** Quote this document: Decentralized Cryptocurrency Markets: The Time Crystal Concept in Atomic Clocks. (April 28, 2023) HackMD. Jules Becci-Morin de la Rivière. Available at: https://hackmd.io/@RIXgTn-rRoasGOobdnzIGg/atomic_clock_quantum_entanglement (Accessed: Month, Day, YYYY). *** Copyright © 2023 Jules Becci-Morin de la Riviere. All rights reserved. No part of this document may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without prior written permission from the copyright owner. Any unauthorized use, sharing, reproduction, or distribution is strictly prohibited.