An extension of the Kac ring model

We introduce a unitary dynamics for quantum spins which is an extension of a model introduced by Mark Kac to clarify the phenomenon of relaxation to equilibrium. When the number of spins gets very large, the magnetization satisfies an autonomous equation as function of time with exponentially fast relaxation to the equilibrium magnetization as determined by the microcanonical ensemble. This is proven as a law of large numbers with respect to a class of initial data. The corresponding Gibbs-von Neumann entropy is also computed and its monotonicity in time discussed.Comment: 15 pages, v2 -> v3: minor typographic correctio

Enstrophy dissipation in two-dimensional turbulence

Insight into the problem of two-dimensional turbulence can be obtained by an analogy with a heat conduction network. It allows the identification of an entropy function associated to the enstrophy dissipation and that fluctuates around a positive (mean) value. While the corresponding enstrophy network is highly nonlocal, the direction of the enstrophy current follows from the Second Law of Thermodynamics. An essential parameter is the ratio $T_k = \gamma_k /(\nu k^2)$ of the intensity of driving $\gamma_k>0$ as a function of wavenumber $k$, to the dissipation strength $\nu k^2$, where $\nu$ is the viscosity. The enstrophy current flows from higher to lower values of $T_k$, similar to a heat current from higher to lower temperature. Our probabilistic analysis of the enstrophy dissipation and the analogy with heat conduction thus complements and visualizes the more traditional spectral arguments for the direct enstrophy cascade. We also show a fluctuation symmetry in the distribution of the total entropy production which relates the probabilities of direct and inverse enstrophy cascades.Comment: 8 pages, revtex

A meaningful expansion around detailed balance

We consider Markovian dynamics modeling open mesoscopic systems which are driven away from detailed balance by a nonconservative force. A systematic expansion is obtained of the stationary distribution around an equilibrium reference, in orders of the nonequilibrium forcing. The first order around equilibrium has been known since the work of McLennan (1959), and involves the transient irreversible entropy flux. The expansion generalizes the McLennan formula to higher orders, complementing the entropy flux with the dynamical activity. The latter is more kinetic than thermodynamic and is a possible realization of Landauer's insight (1975) that, for nonequilibrium, the relative occupation of states also depends on the noise along possible escape routes. In that way nonlinear response around equilibrium can be meaningfully discussed in terms of two main quantities only, the entropy flux and the dynamical activity. The expansion makes mathematical sense as shown in the simplest cases from exponential ergodicity.Comment: 19 page

Non-equilibrium stationary state of a two-temperature spin chain

A kinetic one-dimensional Ising model is coupled to two heat baths, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($$). Spin flips occur with Glauber-type rates generalised to the case of two temperatures. Driven by the temperature differential, the spin chain settles into a non-equilibrium steady state which corresponds to the stationary solution of a master equation. We construct a perturbation expansion of this master equation in terms of the temperature difference and compute explicitly the first two corrections to the equilibrium Boltzmann distribution. The key result is the emergence of additional spin operators in the steady state, increasing in spatial range and order of spin products. We comment on the violation of detailed balance and entropy production in the steady state.Comment: 11 pages, 1 figure, Revte

BNIP3 supports melanoma cell migration and vasculogenic mimicry by orchestrating the actin cytoskeleton

BNIP3 is an atypical BH3-only member of the BCL-2 family of proteins with reported pro-death as well as pro-autophagic and cytoprotective functions, depending on the type of stress and cellular context. In line with this, the role of BNIP3 in cancer is highly controversial and increased BNIP3 levels in cancer patients have been linked with both good as well as poor prognosis. In this study, using small hairpin RNA (shRNA) lentiviral transduction to stably knockdown BNIP3 (BNIP3-shRNA) expression levels in melanoma cells, we show that BNIP3 supports cancer cell survival and long-term clonogenic growth. Although BNIP3-shRNA increased mitochondrial mass and baseline levels of reactive oxygen species production, which are features associated with aggressive cancer cell behavior, it also prevented cell migration and completely abolished the ability to form a tubular-like network on matrigel, a hallmark of vasculogenic mimicry (VM). We found that this attenuated aggressive behavior of these melanoma cells was underscored by severe changes in cell morphology and remodeling of the actin cytoskeleton associated with loss of BNIP3. Indeed, BNIP3-silenced melanoma cells displayed enhanced formation of actin stress fibers and membrane ruffles, while lamellopodial protrusions and filopodia, tight junctions and adherens junctions were reduced. Moreover, loss of BNIP3 resulted in re-organization of focal adhesion sites associated with increased levels of phosphorylated focal adhesion kinase. Remarkably, BNIP3 silencing led to a drop of the protein levels of the integrin-associated protein CD47 and its downstream signaling effectors Rac1 and Cdc42. These observations underscore that BNIP3 is required to maintain steady-state levels of intracellular complexes orchestrating the plasticity of the actin cytoskeleton, which is integral to cell migration and other vital processes stimulating cancer progression. All together these results unveil an unprecedented pro-tumorigenic role of BNIP3 driving melanoma cell's aggressive features, like migration and VM