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Current fluctuations for the one-dimensional totally asymmetric exclusion process (TASEP) connected to reservoirs of particles, and their large scale limit to the KPZ fixed point in finite volume, are studied using exact methods. Focusing on the maximal current phase for TASEP, corresponding to infinite boundary slopes for the KPZ height field, we obtain for general initial condition an exact expression for the late time correction to stationarity, involving extreme value statistics of Brownian paths. In the special cases of stationary and narrow wedge initial conditions, a combination of Bethe ansatz and numerical conjectures alternatively provide fully explicit exact expressions.
The Riemann surface associated with counting the current between two states of an underlying Markov process is hyperelliptic. We explore the consequences of this property for the time-dependent probability of that current for Markov processes with generic transition rates. When the system is prepared in its stationary state, the relevant meromorphic differential is in particular fully characterized by the precise identification of all its poles and zeroes.
After reviewing the peculiar thermodynamics and statistical mechanics of self-gravitating systems, we consider the case of a “binary star” consisting of two particles of size a in gravitational interaction in a box of radius R. The caloric curve of this system displays a region of negative specific heat in the microcanonical ensemble, which is replaced by a first-order phase transition in the canonical ensemble. The free energy viewed as a thermodynamic potential exhibits two local minima that correspond to two metastable states separated by an unstable maximum forming a barrier of potential. By introducing a Langevin equation to model the interaction of the particles with the thermal bath, we study the random transitions of the system between a “dilute” state, where the particles are well separated, and a “condensed” state, where the particles are bound together. We show that the evolution of the system is given by a Fokker–Planck equation in energy space and that the lifetime of a metastable state is given by the Kramers formula involving the barrier of free energy. This is a particular case of the theory developed in a previous paper (Chavanis, 2005) for N Brownian particles in gravitational interaction associated with the canonical ensemble. In the case of a binary star (N=2), all the quantities can be calculated exactly analytically. We compare these results with those obtained in the mean field limit N→+∞.
In this paper, we review and compare the stochastic quantum mechanics of Nelson and the scale relativity theory of Nottale. We consider both nonrelativistic and relativistic frameworks and include the electromagnetic field. These theories propose a derivation of the Schrödinger and Klein–Gordon equations from microscopic processes. We show their formal equivalence. Specifically, we show that the real and imaginary parts of the complex Lorentz equation in Nottale’s theory are equivalent to the Nelson equations, which are themselves equivalent to the Madelung and de Broglie hydrodynamical representations of the Schrödinger and Klein–Gordon equations, respectively. We discuss the different physical interpretations of the Nelson and Nottale theories and stress their strengths and weaknesses. We mention potential applications of these theories to dark matter.
Biohybrid systems in which robotic lures interact with animals have become compelling tools for probing and identifying the mechanisms underlying collective animal behavior. One key challenge lies in the transfer of social interaction models from simulations to reality, using robotics to validate the modeling hypotheses. This challenge arises in bridging what we term the 'biomimicry gap', which is caused by imperfect robotic replicas, communication cues and physics constraints not incorporated in the simulations, that may elicit unrealistic behavioral responses in animals. In this work, we used a biomimetic lure of a rummy-nose tetra fish (Hemigrammus rhodostomus) and a neural network (NN) model for generating biomimetic social interactions. Through experiments with a biohybrid pair comprising a fish and the robotic lure, a pair of real fish, and simulations of pairs of fish, we demonstrate that our biohybrid system generates social interactions mirroring those of genuine fish pairs. Our analyses highlight that: 1) the lure and NN maintain minimal deviation in real-world interactions compared to simulations and fish-only experiments, 2) our NN controls the robot efficiently in real-time, and 3) a comprehensive validation is crucial to bridge the biomimicry gap, ensuring realistic biohybrid systems.
Sujets
Diffusion
Cosmological model
Fermions
Collective intelligence
General relativity
Entropy
Energy high
Mass density
Cosmology
Physique statistique
Scalar field
Kinetic theory
Dark matter halo
Gravitation collapse
Collective behaviour
Energy internal
Dissipation
Gravitation self-force
Energy density
Cosmological constant
Collapse
Denaturation
Nonlinear
9530Sf
Thermodynamics
Catastrophe theory
Effect relativistic
Bethe ansatz
Smoluchowski-Poisson
Gravitational collapse
Nanofiltration
Mouvement brownien
Mass
Atmosphere
Turbulence
Transition vitreuse
Collective behavior
Competition
Equation of state
Quantum mechanics
Euler-Maclaurin
Field theory scalar
Structure
9536+x
Bose–Einstein condensates
Statistical mechanics
Expansion acceleration
Effondrement gravitationnel
Keller-Segel
Distributed Control
Axion star
Gas Chaplygin
Quantum chromodynamics axion
Black hole
9880-k
TASEP
Dark matter
Axion
Chemotaxis
Brownian motion
Halo
Computational modeling
Phase separation
Collisionless stellar-systems
Bose-Einstein
DNA
Hydrodynamics
Computational modelling
Einstein
Nonrelativistic
Marcheur aléatoire
9862Gq
Galaxy
Density
Dark matter theory
Wave function
9535+d
Gravitation
Stability
Fokker-Planck
Collective motion
Dark matter density
Scattering length
Evaporation
Formation
Asymptotic behavior
Current fluctuations
Dark matter fuzzy
Condensation Bose-Einstein
Smoluchowski equation
Random walker
Electromagnetic
Pressure
Chemotaxie
Fermi gas
Dark matter condensation
Dark energy
Rotation
Critical phenomena
Numerical calculations