A team of researchers proposes a method for proving logarithmic Sobolev inequalities (both in their L² and modified forms) with constants independent of system size for quantum Gibbs samplers whose Lindblad generators satisfy Kubo-Martin-Schwinger (KMS) detailed balance. The result addresses an open problem in the theory of quantum relaxation: ensuring that convergence to the Gibbs state does not degrade as the number of particles or degrees of freedom in the system grows.

The starting point is establishing the L² logarithmic Sobolev inequality by transporting it along a temperature-dependent path running from the infinite-temperature product state to the target Gibbs state. Throughout this process, a size-independent decay rate for the sandwiched Rényi-2 divergence is maintained. A tensor-power argument, combined with the quantum asymptotic equipartition property (AEP), then transfers this decay bound to relative entropy, yielding the modified logarithmic Sobolev inequality.

The resulting framework is general and is applied to two concrete regimes: one-dimensional quantum spin chains at any finite temperature, and finite-range quantum spin systems at sufficiently high temperature in any fixed dimension. In both cases, size-independent constants are obtained, guaranteeing uniform relaxation toward equilibrium.

The implications are relevant both for quantum simulation and for the design of quantum sampling algorithms: a size-independent constant ensures that the mixing time does not diverge with the number of qubits or spins, a key condition for the efficiency of thermal-state preparation routines. The work also opens the door to extending the method to other temperature regimes and to systems with long-range interactions.