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Thermodynamical properties of cellular automata

Bertolani, Luca LU (2020) FYSK02 20202
Mathematical Physics
Department of Physics
Abstract
Cellular automata are a set of discrete computational models whose evolution is defined by neighbourhood rules and are used to simulate many complex systems in physics and science. In this work, statistical mechanics and thermodynamics in and out of equilibrium are used to develop a five-class classification scheme for two-dimensional cellular automata. Thermodynamical variables and potentials will be derived and computed according to three different approaches to determine if a cellular automaton rule is representing a system akin to the ideal gas, in or out of the thermodynamical equilibrium.
Popular Abstract
Governments, financial systems, wars and pandemics are the result of local interactions between human beings, or at least that was the case before the internet.
Just like human societies, cellular automata also develop into complex and seemingly unpredictable states. Maybe by better understanding a simple model such as the cellular automaton we could better understand systems that are way harder to crack. Some scientists even say that cellular automata contain secrets about the most fundamental nature of reality on a quantum level, and should even be considered as a candidate for a theory of everything.

Most of the public is not familiar with cellular automata. Fundamentally a cellular automaton is a model of computation consisting of... (More)
Governments, financial systems, wars and pandemics are the result of local interactions between human beings, or at least that was the case before the internet.
Just like human societies, cellular automata also develop into complex and seemingly unpredictable states. Maybe by better understanding a simple model such as the cellular automaton we could better understand systems that are way harder to crack. Some scientists even say that cellular automata contain secrets about the most fundamental nature of reality on a quantum level, and should even be considered as a candidate for a theory of everything.

Most of the public is not familiar with cellular automata. Fundamentally a cellular automaton is a model of computation consisting of a grid of cells with value zero or one that evolves at each time step. The evolution of each cell is based on local rules that define the value at the next time step based on the values of the cells next to it. The main point here is that every interaction is local.

The same property of locality is shared by other systems. In a magnet, the final magnetisation comes from the interaction between the single atoms and in gasses the properties come from the collisions between the molecules.
Think about the air in your room, every single molecule is doing its own thing and wiggling around, colliding with other molecules at a very high speed and producing what you experience as air. It is impossible to keep track of all of them, but statistical measures can give you the information you really need, such as temperature and pressure.

By using the statistical measures of the most well-understood complex systems (thermodynamical systems) to study and create a framework for one of the most basic complex system (cellular automaton), it could be possible to generalize the results to systems that are more complex so we could reach towards a better understanding of them. This thesis is aimed at trying to build the foundations to follow that direction. (Less)
Please use this url to cite or link to this publication:
author
Bertolani, Luca LU
supervisor
organization
course
FYSK02 20202
year
type
M2 - Bachelor Degree
subject
keywords
Thermodynamics, Statistical, Mechanics, Cellular, automata, chaos, complex, matrix, computational, mathematical, 2d, two, dimensional, program, code, python, ising, teaching, ideal, gas, partition, function, equilibrium, non-equilibrium, classification, neighbourhood, local
language
English
id
9040510
date added to LUP
2021-02-18 09:02:36
date last changed
2021-02-18 09:03:49
@misc{9040510,
  abstract     = {{Cellular automata are a set of discrete computational models whose evolution is defined by neighbourhood rules and are used to simulate many complex systems in physics and science. In this work, statistical mechanics and thermodynamics in and out of equilibrium are used to develop a five-class classification scheme for two-dimensional cellular automata. Thermodynamical variables and potentials will be derived and computed according to three different approaches to determine if a cellular automaton rule is representing a system akin to the ideal gas, in or out of the thermodynamical equilibrium.}},
  author       = {{Bertolani, Luca}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Thermodynamical properties of cellular automata}},
  year         = {{2020}},
}