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We investigate the nonequilibrium stationary states of systems consisting of chemical reactions among molecules of several chemical species. To this end we introduce and develop a stochastic formulation of nonequilibrium thermodynamics of…

Statistical Mechanics · Physics 2018-07-04 Tânia Tomé , Mário J. de Oliveira

Far-from-equilibrium thermodynamics underpins the emergence of life, but how has been a long-outstanding puzzle. Best candidate theories based on the maximum entropy production principle could not be unequivocally proven, in part due to…

Quantitative Methods · Quantitative Biology 2017-10-10 Robert G. Endres

Computer simulations generate trajectories at a single, well-defined thermodynamic state point. Statistical reweighting offers the means to reweight static and dynamical properties to different equilibrium state points by means of analytic…

Computational Physics · Physics 2019-12-25 Marius Bause , Timon Wittenstein , Kurt Kremer , Tristan Bereau

Equilibrium rate theories play a crucial role in understanding rare, reactive events. However, they are inapplicable to a range of irreversible processes in systems driven far from thermodynamic equilibrium like active and biological…

Statistical Mechanics · Physics 2025-10-21 Eric R. Heller , David T. Limmer

In this paper, the applicability of the entropy method for the trend towards equilibrium for reaction-diffusion systems arising from first order chemical reaction networks is studied. In particular, we present a suitable entropy structure…

Analysis of PDEs · Mathematics 2016-12-19 Klemens Fellner , Wolfgang Prager , Bao Q. Tang

Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…

Statistical Mechanics · Physics 2015-10-28 Purushottam D. Dixit

We consider a system of reaction-diffusion equations in a bounded interval of the real line, with emphasis on the metastable dynamics, whereby the time-dependent solution approaches the steady state in an asymptotically exponentially long…

Analysis of PDEs · Mathematics 2016-06-27 Marta Strani

The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…

Statistical Mechanics · Physics 2020-08-21 Gil Ariel , Haim Diamant

We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. It is a new…

Analysis of PDEs · Mathematics 2007-05-23 Stephane Genieys , Vitaly Volpert , Pierre Auger

This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…

Analysis of PDEs · Mathematics 2026-05-07 Théo André , Szymon Cygan , Anna Marciniak-Czochra , Finn Münnich

Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…

Optimization and Control · Mathematics 2022-09-13 Michelle S. Chong

The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…

Pattern Formation and Solitons · Physics 2022-07-11 Robert A. Van Gorder , Václav Klika , Andrew L. Krause

Non-reciprocal interactions are present in many systems out of equilibrium. The rate of entropy production is a measure that quantifies the time irreversibility of a system, and thus how far it is from equilibrium. In this work, we…

Statistical Mechanics · Physics 2022-11-28 Ziluo Zhang , Rosalba Garcia-Millan

Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…

Statistical Mechanics · Physics 2019-05-29 Joseph W. Baron , Tobias Galla

In nature stationary nonequilibrium systems cannot exist on their own, rather they need to be driven from outside in order to keep them away from equilibrium. While the internal mean entropy of such stationary systems is constant, the…

Statistical Mechanics · Physics 2013-10-03 Somayeh Zeraati , Farhad H. Jafarpour , Haye Hinrichsen

The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…

Pattern Formation and Solitons · Physics 2019-11-06 Michal Kozák , Eamonn A Gaffney , Václav Klika

The stochastic entropy generated during the evolution of a system interacting with an environment may be separated into three components, but only two of these have a non-negative mean. The third component of entropy production is…

Statistical Mechanics · Physics 2013-05-30 Ian J. Ford , Richard E. Spinney

Transition pathways of stochastic dynamical systems are typically approximated by instantons. Here we show, using a dynamical system containing two competing pathways, that at low-to-intermediate temperatures, instantons can fail to capture…

Statistical Mechanics · Physics 2022-08-05 Lukas Kikuchi , Ronojoy Adhikari , Julian Kappler

We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…

Pattern Formation and Solitons · Physics 2010-11-15 A. V. Straube , A. Pikovsky

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of…

Analysis of PDEs · Mathematics 2016-07-15 Anna Marciniak-Czochra , Grzegorz Karch , Kanako Suzuki