Entropy-stable formulations based on summation-by-parts (SBP) operators provide a general framework for the construction of robust high-order methods for nonlinear partial differential equations. In this talk, we present a new class of efficient entropy-stable discontinuous spectral-element methods of arbitrary order on curved triangular and tetrahedral meshes using tensor-product SBP operators in collapsed coordinates. Such operators, which were previously used in [1] to obtain energy-stable discretizations for linear problems, are employed within a weight-adjusted modal flux-differencing formulation based on the work of Chan and Wilcox [2] in order to obtain efficient entropy-stable schemes for nonlinear hyperbolic systems of conservation laws. Exploiting sum factorization in the evaluation of tensor-product operators in collapsed coordinates (as described, for example, by Karniadakis and Sherwin [3]) as well as exploiting the sparsity of the SBP operator matrices in flux differencing then enables the evaluation of the time derivative in O(p^{d+1}) floating-point operations, where p is the polynomial degree of the discretization and d is the number of spatial dimensions. The proposed approach significantly reduces the number of required entropy-conservative two-point flux evaluations relative to entropy-stable formulations based on (non-tensor-product) multidimensional SBP operators, particularly at high polynomial degrees, while providing the same provable conservation, free-stream preservation, and entropy stability properties offered by such existing schemes. In addition to a discussion of the theoretical and algorithmic aspects of the proposed methods, we demonstrate their accuracy and robustness through a series of numerical experiments involving the solution of the compressible Euler equations. [1] T. Montoya and D. W. Zingg, “Efficient tensor-product spectral-element operators with the summation-by-parts property on curved triangles and tetrahedra,” Preprint, arXiv:2306.05975 [math.NA], 2023. [2] J. Chan and L. C. Wilcox, “On discretely entropy stable weight-adjusted discontinuous Galerkin methods: Curvilinear meshes,” Journal of Computational Physics, vol. 378, pp. 366–393, 2019. [3] G. E. Karniadakis and S. J. Sherwin, Spectral/hp Element Methods for Computational Fluid Dynamics, 2nd ed. Oxford University Press, 2005.