59 problems

In kinetic roughening, let $C_\mathrm{t}(t_1,t_2)$ be the connected two-time correlation function and suppose its rescaled form has the long-time-ratio decay…

Let $R$ be the Reynolds number for a periodically forced Navier–Stokes fluid, let $\mu_R$ be the probability distribution describing the time-average statistics of the irreversible…

Let such measures be invariant measures of systems with a stochastic dynamics, and suppose that they have no detailed balance. In the spin-flip setting, consider non-reversible pro…

Universality conjecture. Throughout phases A and B,

Finite-system conductivity conjecture. $\kappa_N$ and, respectively, $\tilde\kappa_N$, should have the same asymptotic behavior as the conductivity defined in that nonequilibrium s…

Boundary-contribution conjecture. Since the Jensen–Varadhan functional can be interpreted as the bulk limit of the WASEP large-deviation functional, equations (LD boundary 1) and (…

In the kinetic spherical model, let $g(t)$ be the Lagrange multiplier, let $d$ be the spatial dimension, and let $C_1$ and $C_2$ be constants. For sufficiently long times, the Lagr…

The pair contact process with diffusion (PCPD) is a one-dimensional reaction-diffusion model in which particles diffuse and pairs can annihilate or create particles; the preceding…

Let a nonequilibrium steady state (NESS) on a dense network have entropy production rate $\sigma_{\mathrm{NESS}}$, and let … be the minimal entropy production over probability dist…

Consider a finite multi-floor TASEP with $c\ge 1$ floors and attempted particle arrival and departure rates $\alpha>0$ and $\beta>0$. Let … and let … Assume condition (a): $L^*$ co…

Dirichlet hydrodynamic-limit conjecture. For $\theta<1$, the empirical density should be described in the hydrodynamic limit by this equation with Dirichlet boundary conditions.

Let a Hamiltonian dynamical system exhibit mixed chaos, with chaotic trajectories and islands of regularity in its phase space. Suppose the system is weakly coupled to a thermal ba…

Dissipative dressing conjecture. On the basis of numerical studies, the NESS has the form

Let $L$ denote the system size and let $\mathcal{C}_{t}$ be the critical region at time $t$. In equilibrium, the pointer traverses the system and the critical region on the corresp…

Consider a nonequilibrium network in which transition rates on one or more edges are externally controlled, and let the stationary currents be the corresponding steady-state edge c…

Let $c_{\ell}$ denote the coefficients in the expansion of the stationary normalization near the relevant limit, and let $J$ be the late-time average of $Q_t/t$. Sign conjecture. A…

Let $\mathcal{C}>5$ be the upper cell order, and let $\bar{\eta}_{i,j}$ denote the finite fluxes determined by the steady-state equations. A steady state satisfies detailed balance…

Local-equilibrium sharpness conjecture. The scale $R_n$ is the largest scale at which one should expect the NESS to behave as a local equilibrium.

Let $\mathfrak A_{\mathrm{ql}}$ be the algebra of quasilocal operators and let…

Fourier-law conjecture. Fourier law should be valid for a dilute gas maintained out of equilibrium by reservoirs.

Skewness lower-bound conjecture. For fixed affinity $A$ and number of states $\Omega$, the skewness satisfies

Exponential degeneracy conjecture. Each eigenvalue in orbital $p$ has degeneracy $2^{p-1}$. This predicts an exponentially growing many-body degeneracy in the higher orbital sector…

General-validity conjecture. This formula holds generally, even when the compatibility condition $e^{i(\phi+\pi/2)L}=1$ is not satisfied. The formula is established in the compatib…

Consider a quantum anharmonic chain coupled to baths, with $b1$-FPUT, KG, or $b2$-FPUT nonlinearities, and let the nonlinear coupling be treated perturbatively. A nonequilibrium st…

Consider a quantum anharmonic chain with $b1$-FPUT, $b2$-FPUT, or KG nonlinearities, treated perturbatively in weak nonlinear coupling. Let the nonequilibrium steady-state (NESS) t…