State space vs phase space

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.

1. Is phase space the same as state space?
2. What is difference between configuration space and phase space?
3. What is phase space space?
4. What is meant by state space?

Is phase space the same as state space?

A state space could be finite, consisting of just a few points. It could be finite-dimensional, consisting of an infinite number of points forming a smooth manifold, as usually the case in ordinary differential equations and mappings. Such a state space is often called a phase space.

What is difference between configuration space and phase space?

Point in configuration space represents configuration of the system, i.e. positions of the constituent particles. Point in phase space represents state of the system, i.e. positions and velocities of the constituent particles together.

What is phase space space?

In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables.

What is meant by state space?

A state space is the set of all possible configurations of a system. It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory.