The paper by Maldacena, Shenker, and Stanford conjectures a sharp bound on the rate of chaos growth in thermal quantum systems with a large number of degrees of freedom. Chaos is diagnosed using an out-of-time-order correlation function, which is related to the commutator of operators separated in time. The conjecture states that the influence of chaos on this correlator can develop no faster than exponentially, with a Lyapunov exponent \(\lambda_L \leq 2\pi k_B T / \hbar\). The authors provide a mathematical argument based on plausible physical assumptions to support this conjecture. The paper discusses the motivation for the conjecture, including the study of large \(N\) gauge theories and holographic calculations in Einstein gravity. It also explores the implications of the conjecture in various systems, such as large \(N\) systems, extended local systems, and semiclassical billiards. The authors show that the bound holds for systems with a large hierarchy between the scrambling and dissipation timescales, and provide examples to illustrate the bound's applicability. The paper concludes with a discussion of the implications of the conjecture, including its connection to the scattering bound in Rindler space and the possibility that systems saturating the bound might have an Einstein gravity dual.The paper by Maldacena, Shenker, and Stanford conjectures a sharp bound on the rate of chaos growth in thermal quantum systems with a large number of degrees of freedom. Chaos is diagnosed using an out-of-time-order correlation function, which is related to the commutator of operators separated in time. The conjecture states that the influence of chaos on this correlator can develop no faster than exponentially, with a Lyapunov exponent \(\lambda_L \leq 2\pi k_B T / \hbar\). The authors provide a mathematical argument based on plausible physical assumptions to support this conjecture. The paper discusses the motivation for the conjecture, including the study of large \(N\) gauge theories and holographic calculations in Einstein gravity. It also explores the implications of the conjecture in various systems, such as large \(N\) systems, extended local systems, and semiclassical billiards. The authors show that the bound holds for systems with a large hierarchy between the scrambling and dissipation timescales, and provide examples to illustrate the bound's applicability. The paper concludes with a discussion of the implications of the conjecture, including its connection to the scattering bound in Rindler space and the possibility that systems saturating the bound might have an Einstein gravity dual.