Energy hypersurface in a phase space (statistical physics)

In summary, an energy hypersurface in a phase space is a mathematical representation of all possible energy states of a physical system. It is related to statistical physics as it describes the state of a system and helps analyze the behavior of large systems. Studying energy hypersurfaces allows us to understand complex systems and predict their future states. They are calculated using mathematical equations and can be visualized using computer simulations.
  • #1
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what is the reason for that the energy hypersurfaces in a phase space, which belong to systems with constant energy are closed? ( see picture )
237D2118-2CA1-4598-8FEF-7CF73AA8F22C.jpeg
 
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  • #2
If not closed, there would be no border between higher energy region and lower energy region. No energy contour. No grad. No force.
 

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