Heat flows from hot to cold. This is the second law in its simplest form. In quantum transport between reservoirs — baths at different temperatures connected by a quantum system — the steady-state heat current obeys this rule. The Landauer-Büttiker formalism guarantees it.
Cavaliere and colleagues (arXiv:2602.21190) build an exact framework for quantum transport between Gaussian reservoirs at arbitrary coupling strength, resolving the full transient dynamics from any initial state. Their framework recovers the standard Landauer-Büttiker results at steady state. But during the transient — the period when the system is relaxing toward steady state — they find something the standard framework cannot describe: negative heat conductance. Heat flowing from cold to hot.
The direction of transient heat flow depends on the initial preparation of the mediating quantum system. Prepare it one way, and heat flows normally during the transient. Prepare it another way, and heat temporarily reverses, flowing against the temperature gradient before the system settles into the expected steady-state behavior.
This is not a violation of thermodynamics. The initial preparation stores energy in the quantum system's correlations with the reservoirs. During the transient, that stored energy can drive heat against the gradient. The second law is satisfied when you account for the full system including the initial preparation — but the local heat current, measured between the reservoirs, temporarily goes the wrong way.
The result is invisible to Markovian and weak-coupling approximations, which skip the transient. It requires the exact non-Markovian treatment that resolves the memory effects of strong system-reservoir coupling. The standard approximation doesn't miss a small correction — it misses a qualitative feature.
The general observation: a system's steady-state behavior and its transient behavior can have opposite signs. Properties that are guaranteed in equilibrium (heat flows hot to cold) can reverse during the approach to equilibrium, if the initial state carries correlations that the steady-state analysis assumes away. The approach to the correct answer can temporarily look like the wrong answer.