A sticky business: the status of the conjectured viscosity/entropy density bound

TL;DR

The paper critically analyzes proposed universal lower bounds on the shear viscosity to entropy density ratio $\eta/s$, showing that several broad variants fail due to consistent counterexamples. It classifies conjecture variants by underlying theory class and fluid stability, then constructs explicit counterexamples across these classes: a multi-species nonrelativistic gas (class 1), a single-species resonant gas (class 2), and a heavy-meson gas in a UV-complete, large-$N_c$ limit (class 3b). The results suggest that only a narrow, metastable regime (class 3a/3′) might survive, with empirical support largely limited to fluids not falling into these pathological constructions. If a universal bound exists, it would likely require new physics beyond conventional quantum mechanics and quantum field theory, potentially linked to quantum gravity or holographic considerations.

Abstract

There have been a number of forms of a conjecture that there is a universal lower bound on the ratio, eta/s, of the shear viscosity, eta, to entropy density, s, with several different domains of validity. We examine the various forms of the conjecture. We argue that a number of variants of the conjecture are not viable due to the existence of theoretically consistent counterexamples. We also note that much of the evidence in favor of a bound does not apply to the variants which have not yet been ruled out.

Figures (4)

• Figure 1: As a variational ansatz, we picture the fluid's volume to be divided into cells with exactly two particles in each cell.
• Figure 2: A close up view of one particular cell with the drawn circle representing the constraints on the particles wave function imposed by the boundary conditions.
• Figure 3: Graph of the calculated partition function and a linear best-fit to the data.
• Figure 4: Graph of calculated logarithm of the parition function and a logarithmic best-fit to the data.