  In quantum systems, entropy production is typically defined as the quantum
relative entropy between two states. This definition provides an upper bound
for any flux (of particles, energy, entropy, etc.) of bounded observables,
which proves especially useful near equilibrium. However, this bound tends to
be irrelevant in general nonequilibrium situations. We propose a new upper
bound for such fluxes in terms of quantum relative entropy, applicable even far
from equilibrium and in the strong coupling regime. Additionally, we compare
this bound with Monte Carlo simulations of random qubits with coherence, as
well as with a model of two interacting nuclear spins.

Quantum Physics