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Related Concept Videos

Circuit Terminology01:14

Circuit Terminology

An electrical network is a system composed of interconnected elements, such as resistors, capacitors, inductors, and voltage or current sources. Unlike a circuit, an electrical network does not necessarily form a closed path. In other words, while all circuits can be considered networks due to their interconnected nature, not every network qualifies as a circuit.
A circuit, on the other hand, is also an interconnected system of electrical elements but must contain one or more closed paths.
Classification of Systems-II01:31

Classification of Systems-II

Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
Second-Order Circuits01:17

Second-Order Circuits

Integrating two fundamental energy storage elements in electrical circuits results in second-order circuits, encompassing RLC circuits and circuits with dual capacitors or inductors (RC and RL circuits). Second-order circuits are identified by second-order differential equations that link input and output signals.
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
First-Order Circuits01:15

First-Order Circuits

First-order electrical circuits, which comprise resistors and a single energy storage element - either a capacitor or an inductor, are fundamental to many electronic systems. These circuits are governed by a first-order differential equation that describes the relationship between input and output signals.
One common example of a first-order circuit is the RC (resistor-capacitor) circuit. These circuits are used in relaxation oscillators such as neon lamp oscillator circuits. When voltage is...
Classification of Systems-I01:26

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
Signal Flow Graphs01:18

Signal Flow Graphs

Signal-flow graphs offer a streamlined and intuitive approach to representing control systems, providing an alternative to traditional block diagrams. These graphs use branches to symbolize systems and nodes to represent signals, effectively illustrating the relationships and interactions within the system.
In a signal-flow graph, branches denote the system's transfer functions, while nodes represent the signals. The direction of signal flow is indicated by arrows, with the corresponding...

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Effective theories for circuits and automata.

Simon DeDeo1

  • 1Santa Fe Institute, Santa Fe, New Mexico 87501, USA. simon@santafe.edu

Chaos (Woodbury, N.Y.)
|October 7, 2011
PubMed
Summary

This study develops effective theories for complex systems with noise and irreversibility. It shows how system composition can create new theories, but dissipation limits their lifespan.

Area of Science:

  • Complexity Science
  • Theoretical Physics
  • Dynamical Systems

Background:

  • Abstracting effective theories from complex processes is challenging.
  • Dissipation and irreversibility complicate analysis in biological, computational, and social systems.
  • Understanding emergent properties requires robust theoretical frameworks.

Purpose of the Study:

  • To demonstrate the construction of effective theories in systems with irreversibility and noise.
  • To explore how the composition of underlying mechanisms influences emergent theories.
  • To analyze the impact of dissipation on the lifespan of emergent structures.

Main Methods:

  • Utilizing a dynamical model with underlying feedback.
  • Applying the Krohn-Rhodes theorem to analyze mechanism composition.

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  • Investigating the effects of noise and dissipation on system dynamics.

    • Main Results:

    • Successfully constructed effective theories for systems with irreversibility and noise.
    • The Krohn-Rhodes theorem reveals how mechanism composition drives theoretical innovation.
    • Dissipation and irreversibility fundamentally limit the lifetimes of emergent structures.
    • Noiseless counterparts exhibit enriched group properties on short timescales.

    Conclusions:

    • Effective theories can be abstracted even in the presence of noise and irreversibility.
    • System composition is a key factor in the emergence of novel theoretical properties.
    • The inherent limitations imposed by dissipation necessitate careful consideration of emergent structure stability.