scholarly journals Non-Equilibrium Thermodynamics and Stochastic Dynamics of a Bistable Catalytic Surface Reaction

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 811 ◽  
Author(s):  
Miguel Pineda ◽  
Michail Stamatakis
Keyword(s):  
Steady State ◽  
Entropy Production ◽  
Production Rate ◽  
Surface Reaction ◽  
Stochastic Dynamics ◽  
Reaction System ◽  
Entropy Production Rate ◽  
Minimum Entropy ◽  
Catalytic Surface ◽  
Non Equilibrium

Catalytic surface reaction networks exhibit nonlinear dissipative phenomena, such as bistability. Macroscopic rate law descriptions predict that the reaction system resides on one of the two steady-state branches of the bistable region for an indefinite period of time. However, the smaller the catalytic surface, the greater the influence of coverage fluctuations, given that their amplitude normally scales as the square root of the system size. Thus, one can observe fluctuation-induced transitions between the steady-states. In this work, a model for the bistable catalytic CO oxidation on small surfaces is studied. After a brief introduction of the average stochastic modelling framework and its corresponding deterministic limit, we discuss the non-equilibrium conditions necessary for bistability. The entropy production rate, an important thermodynamic quantity measuring dissipation in a system, is compared across the two approaches. We conclude that, in our catalytic model, the most favorable non-equilibrium steady state is not necessary the state with the maximum or minimum entropy production rate.

scholarly journals Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schlögl model revisited

2008 ◽  
Vol 6 (39) ◽  
pp. 925-940 ◽  
Author(s):  
Melissa Vellela ◽  
Hong Qian
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Chemical Potential ◽  
Reaction System ◽  
Bistable System ◽  
Chemical System ◽  
Entropy Production Rate ◽  
Thermodynamic Quantities ◽  
Full Time ◽  
Non Equilibrium

Schlögl's model is the canonical example of a chemical reaction system that exhibits bistability. Because the biological examples of bistability and switching behaviour are increasingly numerous, this paper presents an integrated deterministic, stochastic and thermodynamic analysis of the model. After a brief review of the deterministic and stochastic modelling frameworks, the concepts of chemical and mathematical detailed balances are discussed and non-equilibrium conditions are shown to be necessary for bistability. Thermodynamic quantities such as the flux, chemical potential and entropy production rate are defined and compared across the two models. In the bistable region, the stochastic model exhibits an exchange of the global stability between the two stable states under changes in the pump parameters and volume size. The stochastic entropy production rate shows a sharp transition that mirrors this exchange. A new hybrid model that includes continuous diffusion and discrete jumps is suggested to deal with the multiscale dynamics of the bistable system. Accurate approximations of the exponentially small eigenvalue associated with the time scale of this switching and the full time-dependent solution are calculated using M atlab . A breakdown of previously known asymptotic approximations on small volume scales is observed through comparison with these and Monte Carlo results. Finally, in the appendix section is an illustration of how the diffusion approximation of the chemical master equation can fail to represent correctly the mesoscopically interesting steady-state behaviour of the system.

scholarly journals Testing the Steady-State Fluctuation Relation in the Solar Photospheric Convection

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 716
Author(s):  
Giorgio Viavattene ◽  
Giuseppe Consolini ◽  
Luca Giovannelli ◽  
Francesco Berrilli ◽  
Dario Del Moro ◽  
...  
Keyword(s):  
Steady State ◽  
Entropy Production ◽  
Production Rate ◽  
Local Level ◽  
Entropy Production Rate ◽  
Quasi Steady State ◽  
The Sun ◽  
Statistical Features ◽  
Local Entropy ◽  
Fluctuation Relation

The turbulent thermal convection on the Sun is an example of an irreversible non-equilibrium phenomenon in a quasi-steady state characterized by a continuous entropy production rate. Here, the statistical features of a proxy of the local entropy production rate, in solar quiet regions at different timescales, are investigated and compared with the symmetry conjecture of the steady-state fluctuation theorem by Gallavotti and Cohen. Our results show that solar turbulent convection satisfies the symmetries predicted by the fluctuation relation of the Gallavotti and Cohen theorem at a local level.

Computational Intelligence for Robust Control Algorithms of Complex Dynamic Systems with Minimum Entropy Production

1999 ◽  
Vol 3 (2) ◽  
pp. 82-98 ◽  
Author(s):  
S.V. Ulyanov ◽  
◽  
K. Yamafuji ◽  
V.S. Ulyanov ◽  
I. Kurawaki ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Entropy Production ◽  
Production Rate ◽  
Dynamic Systems ◽  
Fitness Function ◽  
Object Motion ◽  
Entropy Production Rate ◽  
Minimum Entropy ◽  
Minimum Entropy Production

Our thermodynamic approach to the study and design of robust optimal control processes in nonlinear (in general global unstable) dynamic systems used soft computing based on genetic algorithms with a fitness function as minimum entropy production. Control objects were nonlinear dynamic systems involving essentially nonlinear stochastic differential equations. An algorithm was developed for calculating entropy production rate in control object motion and in control systems. Part 1 discusses relation of the Lyapunov function (measure of stability) and the entropy production rate (physical measure of controllability). This relation was used to describe the following qualitative properties and important relations: dynamic stability motion (Lyapunov function), Lyapunov exponent and Kolmogorov-Sinai entropy, physical entropy production rates, and symmetries group representation in essentially nonlinear systems as coupled oscillator models. Results of computer simulation are presented for entropy-like dynamic behavior for typical benchmarks of dynamic systems such as Van der Pol, Duffing, and Holmes-Rand, and coupled oscillators. Parts 2 and 3 discuss the application of this approach to simulation of dynamic entropy-like behavior and optimal benchmark control as a 2-link manipulator in a robot for service use and nonlinear systems under stochastic excitation.

THE THERMODYNAMIC DESCRIPTION OF HETEROGENEOUS DISSIPATIVE SYSTEMS BY VARIATIONAL METHODS: III. AN APPLICATION OF THE PRINCIPLE OF MINIMUM ENTROPY PRODUCTION TO FLUID DYNAMICS

1964 ◽  
Vol 42 (8) ◽  
pp. 1437-1446 ◽  
Author(s):  
J. S. Kirkaldy
Keyword(s):  
Steady State ◽  
Entropy Production ◽  
Thermodynamic Description ◽  
Free Fall ◽  
Dissipative Systems ◽  
Entropy Production Rate ◽  
Stable Steady State ◽  
Minimum Entropy ◽  
Minimum Entropy Production ◽  
Steady State Rate

The stable free-fall flight of a maple seed gives an exceptionally graphic demonstration of the principle of minimum entropy production. Since the rate of entropy production is proportional to the steady-state rate of loss of potential energy, it is visually obvious that the stable rotary configuration represents a minimum of the entropy production rate relative to an unstable steady-state bomblike trajectory. Regarding this phenomenon as the prototype of many practical steady-state fluid-dynamical systems involving rotational modes, we formally demonstrate the possibility of mathematically defining the stable steady-state configuration by means of this variational principle.

Steady state traffic flow, entropy production rate, temporal fluctuations and fuel consumption

2006 ◽  
Vol 361 (2) ◽  
pp. 630-642 ◽  
Author(s):  
J.A. Montemayor-Aldrete ◽  
P. Ugalde-Vélez ◽  
M. del Castillo-Mussot ◽  
C.A. Vázquez-Villanueva ◽  
G.J. Vázquez ◽  
...  
Keyword(s):  
Steady State ◽  
Entropy Production ◽  
Production Rate ◽  
Fuel Consumption ◽  
Traffic Flow ◽  
Entropy Production Rate ◽  
Temporal Fluctuations
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