Open and Closed Systems: Inputs and Outputs

Open and Closed Systems: Inputs and Outputs

  • Core takeaway from the transcript: all open and closed systems ultimately rely on inputs from the environment and the system’s responses to those inputs.
  • This statement frames system behavior around two pillars: what the system takes in (inputs) and what it does as a result (outputs/responses).
  • It also implies a boundary between the system and its environment, across which signals, matter, or energy can flow depending on the system type.
  • The idea applies across disciplines: thermodynamics, cybernetics, control theory, biology, economics, and social systems.

Key Concepts

  • Open system: a system that exchanges matter, energy, or information with its environment. Inputs come from outside the boundary; outputs affect the environment.
  • Closed system: a system that is isolated from its environment with limited or no exchange of matter or energy. In practice, many so-called closed systems still exchange energy (e.g., heat) but not matter; in some contexts, a strictly closed system means no external inputs.
  • System inputs: stimuli, signals, resources, energy, or information that drive the system’s state and behavior.
  • System responses (outputs): the observable changes, actions, signals, or state transitions produced by the system in reaction to inputs.
  • Boundary and environment: the demarcation that defines what counts as an input versus internal state; the environment is the source/sink for inputs/outputs.
  • Open-loop vs. closed-loop (role of feedback): open-loop systems operate without using outputs to adjust inputs; closed-loop systems use feedback from outputs to influence future inputs.

System Inputs

  • Types of inputs:
    • Energy (e.g., heat, work, electrical energy) E
      ???
    • Matter (e.g., nutrients, air, water)
    • Information (sensor data, signals, commands)
    • Resources (raw materials, capital, time)
    • External conditions (temperature, pressure, market signals)
  • Input vector notation (common in control theory): u(t)\boldsymbol{u}(t) where oldsymbol{u} collects all input signals.
  • Examples:
    • A thermostat-controlled heater receives temperature readings and decides heating level.
    • A plant photosynthesizes based on light and CO₂ availability.
    • A computer program processes input data streams (packets, user commands).
  • Inputs can be deterministic or stochastic and may change over time: $$ oldsymbol{u}(t)
    ightarrow oldsymbol{u}(t) + ext{noise} \