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Piyush Grover
Piyush Grover
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Q: Might there be a reason why stable physical processes would tend to have low-dimensional phase spaces.

Yes. TheOne reason is physical processes have dissipation. E.g., turbulence is "known" to be chaotic dynamics on a low dimensional manifold (i.e., strange attractor) in the infinite dimensional phase space (of $L^2$ velocity fields). Even its dimension can be estimated. See for example:

Doering, Charles R., and John D. Gibbon. "Note on the Constantin-Foias-Temam attractor dimension estimate for two-dimensional turbulence." Physica D: Nonlinear Phenomena 48.2-3 (1991): 471-480.

.

Q: Might there be a reason why stable physical processes would tend to have low-dimensional phase spaces.

Yes. The reason is physical processes have dissipation. E.g., turbulence is "known" to be chaotic dynamics on a low dimensional manifold (i.e., strange attractor) in the infinite dimensional phase space (of $L^2$ velocity fields). Even its dimension can be estimated. See for example:

Doering, Charles R., and John D. Gibbon. "Note on the Constantin-Foias-Temam attractor dimension estimate for two-dimensional turbulence." Physica D: Nonlinear Phenomena 48.2-3 (1991): 471-480.

.

Q: Might there be a reason why stable physical processes would tend to have low-dimensional phase spaces.

Yes. One reason is physical processes have dissipation. E.g., turbulence is "known" to be chaotic dynamics on a low dimensional manifold (i.e., strange attractor) in the infinite dimensional phase space (of $L^2$ velocity fields). Even its dimension can be estimated. See for example:

Doering, Charles R., and John D. Gibbon. "Note on the Constantin-Foias-Temam attractor dimension estimate for two-dimensional turbulence." Physica D: Nonlinear Phenomena 48.2-3 (1991): 471-480.

.

Source Link
Piyush Grover
Piyush Grover
  • 2.3k
  • 1
  • 23
  • 44

Q: Might there be a reason why stable physical processes would tend to have low-dimensional phase spaces.

Yes. The reason is physical processes have dissipation. E.g., turbulence is "known" to be chaotic dynamics on a low dimensional manifold (i.e., strange attractor) in the infinite dimensional phase space (of $L^2$ velocity fields). Even its dimension can be estimated. See for example:

Doering, Charles R., and John D. Gibbon. "Note on the Constantin-Foias-Temam attractor dimension estimate for two-dimensional turbulence." Physica D: Nonlinear Phenomena 48.2-3 (1991): 471-480.

.