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We study analytically and numerically a bistable reaction-diffusion equation on an arbitrary finite network. We prove that stable fixed points (multi-fronts) exist for any configuration as long as the diffusion is small. We also study fold…

Adaptation and Self-Organizing Systems · Physics 2015-06-22 J. -G. Caputo , G. Cruz-Pacheco , P. Panayotaros

We study the situation in which the distribution of temperature a body is due to its interaction with radiation. We consider the boundary value problem for the stationary radiative transfer equation under the assumption of the local…

Analysis of PDEs · Mathematics 2025-06-02 Elena Demattè , Juan J. L. Velázquez

Advances in experimental techniques enable the precise manipulation of a large variety of active systems, which constantly dissipate energy to sustain nonequilibrium phenomena without any equilibrium equivalent. To design novel materials…

Statistical Mechanics · Physics 2025-06-03 Artur Soriani , Elsen Tjhung , Étienne Fodor , Tomer Markovich

It is known that effects of dissipation or measurement backreaction in postselected quantum trajectories are described by non-Hermitian Hamiltonian, but their consequences in real-time dynamics of many-body systems are yet to be elucidated.…

Quantum Gases · Physics 2023-04-05 Tomoya Hayata , Yoshimasa Hidaka , Arata Yamamoto

We investigate the relation between an applied potential and the corresponding stationary state occupation for nonequilibrium and overdamped diffusion processes. This relation typically becomes long ranged resulting in global changes for…

Statistical Mechanics · Physics 2009-11-05 Christian Maes , Karel Netocny , Bidzina M. Shergelashvili

Nonequilibrium systems, in particular living organisms, are maintained by irreversible transformations of energy that drive diverse functions. Quantifying their irreversibility, as measured by energy dissipation, is essential for…

Statistical Mechanics · Physics 2025-05-21 Qiwei Yu , Pedro E. Harunari

Network science investigates the architecture of complex systems to understand their functional and dynamical properties. Structural patterns such as communities shape diffusive processes on networks. However, these results hold under the…

Physics and Society · Physics 2015-06-26 Jean-Charles Delvenne , Renaud Lambiotte , Luis E. C. Rocha

Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the…

Statistical Mechanics · Physics 2007-05-23 V. Colizza , R. Pastor-Satorras , A. Vespignani

The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…

Adaptation and Self-Organizing Systems · Physics 2020-05-01 E. Heinsalu , D. Navidad Maeso , M. Patriarca

Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…

Soft Condensed Matter · Physics 2017-10-11 Gerald J. Lapeyre , Marco Dentz

In a generalized framework for the Landauer erasure protocol, we study bounds on the heat dissipated in typical nonequilibrium quantum processes. In contrast to thermodynamic processes, quantum fluctuations are not suppressed in the…

Quantum Physics · Physics 2018-05-16 Philip Taranto , Kavan Modi , Felix A. Pollock

Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…

Statistical Mechanics · Physics 2026-03-24 Valentin Anfray , Hong-Yan Shih

Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…

Statistical Mechanics · Physics 2023-05-10 Johan du Buisson , Hugo Touchette

We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…

Analysis of PDEs · Mathematics 2023-10-24 Montie Avery

Using the framework of stochastic thermodynamics we study heat production related to the stochastic motion of a particle driven by repulsive, nonlinear, time-delayed feedback. Recently it has been shown that this type of feedback can lead…

Soft Condensed Matter · Physics 2025-03-07 Robin A. Kopp , Sabine H. L. Klapp

Electro-energy-reaction-diffusion systems are thermodynamically consistent continuum models for reaction-diffusion processes that account for temperature and electrostatic effects in a way that total charge and energy are conserved. The…

Analysis of PDEs · Mathematics 2026-04-09 Katharina Hopf , Michael Kniely , Alexander Mielke

Dissipation anomaly-the persistence of finite energy dissipation in the inviscid limit-is a hallmark of turbulence, sometimes regarded as the "zeroth law" of turbulent flows. Here, we demonstrate that this phenomenon is not exclusive to…

Statistical Mechanics · Physics 2025-11-25 Hiroyoshi Nakano , Yuki Minami

The theoretical and experimental study of energy transfer in photosynthesis has revealed an interesting transport regime, which lies at the borderline between classical transport dynamics and quantum-mechanical interference effects.…

Biological Physics · Physics 2014-02-13 Tobias Kramer , Christoph Kreisbeck

Active systems evade the rules of equilibrium thermodynamics by constantly dissipating energy at the level of their microscopic components. This energy flux stems from the conversion of a fuel, present in the environment, into sustained…

Soft Condensed Matter · Physics 2022-03-15 Étienne Fodor , Robert L. Jack , Michael E. Cates

We consider stationary driven systems in contact with a thermal equilibrium bath. There is a constant (Joule) heat dissipated from the steady system to the environment as long as all parameters are unchanged. As a natural generalization…

Statistical Mechanics · Physics 2020-01-29 Christian Maes , Karel Netocny