What is the difference between phase space and state-space?

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SUMMARY

The discussion clarifies the distinction between state space and phase space in dynamical systems. State space consists of state variables that uniquely define a system's dynamics, while phase space encompasses both coordinates and momenta, specifically in classical mechanics. For example, the state space of an ideal gas is represented by the coordinates (P, V, N), indicating pressure, volume, and number of particles. Understanding these concepts is crucial for analyzing system behavior in various scientific fields.

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  • Understanding of state variables in dynamical systems
  • Familiarity with classical mechanics principles
  • Knowledge of thermodynamic systems
  • Basic grasp of mathematical representation of systems
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student-engineer
In state space, the coordinates are the state variables of a system.So,each point in state space represents a specific value of state variables.Thus,state space representation represents the changes in a dynamical system. The state variables are the minimum number of variables which uniquely define the dynamics of a system. What is the difference between state space and phase space.
 
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The term state space can be used in many contexts, including a thermodynamical system, e.g. the state space of an ideal gas consists of points with coordinates (P,V,N), while the term phase space always means a set of coordinates and momenta of a system in classical mechanics.
 
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