original_query: What is the Fermi–Pasta–Ulam–Tsingou problem?
query: What is the Fermi–Pasta–Ulam–Tsingou problem?
answer: The Fermi–Pasta–Ulam–Tsingou (FPUT) problem is an apparent paradox in chaos theory where complex physical systems exhibit almost perfectly periodic behavior (FPUT recurrence) instead of the expected ergodic behavior (where all vibrational modes appear with equal strength).  While recurrence is easily observed, over much longer periods the system does eventually thermalize.  The problem's unexpected results launched the study of nonlinear systems and highlighted the complexity of nonlinear system behavior.