Poissonian Cellular Potts Models Reveal Nonequilibrium Kinetics of Cell Sorting.

Cellular Potts models are broadly applied across developmental biology and cancer research. We overcome limitations of the traditional approach, which reinterprets a modified Metropolis sampling as ad hoc dynamics, by introducing a physical timescale through Poissonian kinetics and by applying principles of stochastic thermodynamics to separate thermal and relaxation effects from athermal noise and nonconservative forces. Our method accurately describes cell-sorting dynamics in mouse-embryo development and identifies the distinct contributions of nonequilibrium processes, e.g., cell growth and active fluctuations.

Equilibrium and nonequilibrium description of negative temperature states in a one-dimensional lattice using a wave kinetic approach.

We predict negative temperature states in the discrete nonlinear Schödinger (DNLS) equation as exact solutions of the associated wave kinetic equation. Within the wave kinetic approach, we define an entropy that results monotonic in time and reaches a stationary state, that is consistent with classical equilibrium statistical mechanics. We also perform a detailed analysis of the fluctuations of the actions at fixed wave numbers around their mean values. We give evidence that such fluctuations relax to their equilibrium behavior on a shorter timescale than the one needed for the spectrum to reach the equilibrium state. Numerical simulations of the DNLS equation are shown to be in agreement with our theoretical results. The key ingredient for observing negative temperatures in lattices characterized by two invariants is the boundedness of the dispersion relation.

Anomalies and absence of local equilibrium, and universality, in one-dimensional particles systems.

One-dimensional systems are under intense investigation, both from theoretical and experimental points of view, since they have rather peculiar characteristics which are of both conceptual and technological interest. We analyze the dependence of the behavior of one-dimensional, time-reversal invariant, nonequilibrium systems on the parameters defining their microscopic dynamics. In particular, we consider chains of identical oscillators interacting via hard-core elastic collisions and harmonic potentials, driven by boundary Nosé-Hoover thermostats. Their behavior mirrors qualitatively that of stochastically driven systems, showing that anomalous properties are typical of physics in one dimension. Chaos, by itself, does not lead to standard behavior, since it does not guarantee local thermodynamic equilibrium. A linear relation is found between density fluctuations and temperature profiles. This link and the temporal asymmetry of fluctuations of the main observables are robust against modifications of thermostat parameters and against perturbations of the dynamics.

Spatiotemporal chaos and the dynamics of coupled Langmuir and ion-acoustic waves in plasmas.

A simulation study is performed to investigate the dynamics of coupled Langmuir waves (LWs) and ion-acoustic waves (IAWs) in an unmagnetized plasma. The effects of dispersion due to charge separation and the density nonlinearity associated with the IAWs are considered to modify the properties of Langmuir solitons, as well as to model the dynamics of relatively large amplitude wave envelopes. It is found that the Langmuir wave electric field, indeed, increases by the effect of ion-wave nonlinearity (IWN). Use of a low-dimensional model, based on three Fourier modes, shows that a transition to temporal chaos is possible, when the length scale of the linearly excited modes is larger than that of the most unstable ones. The chaotic behaviors of the unstable modes are identified by the analysis of Lyapunov exponent spectra. The space-time evolution of the coupled LWs and IAWs shows that the IWN can cause the excitation of many unstable harmonic modes and can lead to strong IAW emission. This occurs when the initial wave field is relatively large or the length scale of IAWs is larger than the soliton characteristic size. Numerical simulation also reveals that many solitary patterns can be excited and generated through the modulational instability of unstable harmonic modes. As time goes on, these solitons are seen to appear in the spatially partial coherence state due to the free ion-acoustic radiation as well as in the state of spatiotemporal chaos due to collision and fusion in the stochastic motion. The latter results in the redistribution of initial wave energy into a few modes with small length scales, which may lead to the onset of Langmuir turbulence in laboratory as well as space plasmas.

Nonequilibrium steady-state fluctuations in actively cooled resonators.

We analyze heat and work fluctuations in the gravitational wave detector AURIGA, modeled as a macroscopic electromechanical oscillator in contact with a thermostat and cooled by an active feedback system. The oscillator is driven to a steady state by the feedback cooling, equivalent to a viscous force. The experimentally measured fluctuations are in agreement with our theoretical analysis based on a stochastically driven Langevin system. The asymmetry of the fluctuations of the absorbed heat characterizes the oscillator's nonequilibrium steady state and reveals the extent to which a feedback cooled system departs from equilibrium in a statistical mechanics perspective.

Fluctuation theorems for entropy production in open systems

We derive a fluctuation theorem to describe entropy fluctuations in steady states of systems with density gradients due to open boundaries. The fluctuations are related to the growth rate of the phase-space density, instead of the phase-space contraction rate. Explicit derivations are presented for a multibaker map, but the arguments are rather general, and should hold for a much wider class of dynamical systems. A comparison with recent results for stochastic systems is also given.

Note on phase space contraction and entropy production in thermostatted Hamiltonian systems.

The phase space contraction and the entropy production rates of Hamiltonian systems in an external field, thermostatted to obtain a stationary state, are considered. While for stationary states with a constant kinetic energy the two rates are formally equal for all numbers of particles N, for stationary states with constant total (kinetic and potential) energy this only obtains for large N. However, in both cases a large number of particles is required to obtain equality with the entropy production rate of Irreversible Thermodynamics. Consequences of this for the positivity of the transport coefficients and for the Onsager relations are discussed. Numerical results are presented for the special case of the Lorentz gas. (c) 1998 American Institute of Physics.