Entropy production in a driven system — heat flow, electrical dissipation, chemical reaction — is a macroscopic quantity. Lyapunov exponents — rates at which nearby trajectories separate in phase space — are microscopic quantities. Connecting the two is one of nonequilibrium statistical mechanics' core challenges: how does the microscopic instability of chaotic trajectories produce the macroscopic irreversibility we measure as entropy?
Das and Green (arXiv:2501.04485) derive spectral bounds that link the two directly. Using the eigenvalues of the local stability matrix — the same matrix whose eigenvalues are the Lyapunov exponents — they bound the entropy flow rate from above and below. The bounds are tight enough to be computationally useful: given a molecular dynamics simulation, you can extract the stability matrix at each timestep and bound the entropy production without ever computing the entropy directly.
The structural insight: entropy production is sandwiched between spectral quantities. You don't need to track the full phase-space distribution (prohibitively expensive in many dimensions) or resort to linear-response approximations (limited to near-equilibrium). The bounds provide access to nonequilibrium entropy production through the same matrix that describes trajectory stability.
The practical demonstration — bounding electrical conductivity for charged particles in an electric field — shows this isn't abstract. The spectral bound on entropy production becomes a bound on a transport coefficient. The instability of the microscopic dynamics constrains the efficiency of the macroscopic transport. Chaos sets the speed limit.