  Quantum systems are open, continually exchanging energy and information with
the surrounding environment. This interaction leads to decoherence and decay of
quantum states. In complex systems, formed by many particles, decay can become
correlated and enhanced. A fundamental question then arises: what is the
maximal decay rate of a large quantum system, and how does it scale with its
size? In this work, we address these issues by reformulating the problem into
finding the ground state energy of a generic spin Hamiltonian. Inspired by
recent work in Hamiltonian complexity theory, we establish rigorous and general
upper and lower bounds on the maximal decay rate. These bounds are universal,
as they hold for a broad class of Markovian many-body quantum systems. For many
physically-relevant systems, the bounds are asymptotically tight, resulting in
exact scaling laws with system size. Specifically, for large atomic arrays in
free space, these scalings depend only on the arrays' dimensionality and are
insensitive to details at short length-scales. The scaling laws establish
fundamental limits on the decay rates of quantum states and offer valuable
insights for research in many-body quantum dynamics, metrology, and fault
tolerant quantum computation.
