  We study aspects of chaos and thermodynamics at strong coupling in a scalar
model using LCT numerical methods. We find that our eigenstate spectrum
satisfies Wigner-Dyson statistics and that the coefficients describing
eigenstates in our basis satisfy Random Matrix Theory (RMT) statistics. At weak
coupling, though the bulk of states satisfy RMT statistics, we find several
scar states as well. We then use these chaotic states to compute the equation
of state of the model, obtaining results consistent with Conformal Field Theory
(CFT) expectations at temperatures above the scale of relevant interactions. We
also test the Eigenstate Thermalization Hypothesis by computing the expectation
value of local operators in eigenstates, and check that their behavior is
consistent with thermal CFT values at high temperatures. Finally, we compute
the Spectral Form Factor (SFF), which has the expected behavior associated with
the equation of state at short times and chaos at long times. We also propose a
new technique for extracting the connected part of the SFF without the need of
disorder averaging by using different symmetry sectors.
