degenerate state or character.
the process of degenerating; decline.
degenerate behavior, especially behavior considered sexually deviant.
Physics. the number of distinct quantum states of a system that have a given energy.

1655–65; degener(ate) + -acy

nondegeneracy, noun, plural nondegeneracies.
predegeneracy, noun
undegeneracy, noun Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
degeneracy (dɪˈdʒɛnərəsɪ)
n , pl -cies
1.  the act or state of being degenerate
2.  the process of becoming degenerate
3.  physics the number of degenerate quantum states of a particular orbital, degree of freedom, energy level, etc

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Word Origin & History

1660s, from degenerate (q.v.).
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
So the electron or neutron degeneracy pressures cannot stop collapse.
If there is anything good about nobility it is that it enforces the necessity
  of avoiding degeneracy.
Nothing so much illustrates this mercy as the wretched degeneracy into which
  the subjects of it were fallen.
If neutron degeneracy pressure is enough to stop gravity, you get a neutron
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