scholarly journals Dissipation Function: Nonequilibrium Physics and Dynamical Systems

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 835
Author(s):  
Salvatore Caruso ◽  
Claudio Giberti ◽  
Lamberto Rondoni
Keyword(s):  
Dynamical Systems ◽  
Particle System ◽  
Dissipation Function ◽  
Physical Models ◽  
Nonequilibrium Molecular Dynamics ◽  
Entropy Production Rate ◽  
Response Theory ◽  
Formal Approach ◽  
Physical Content ◽  
Thermodynamic Potentials

An exact response theory has recently been developed within the field of Nonequilibrium Molecular Dynamics. Its main ingredient is known as the Dissipation Function, Ω. This quantity determines nonequilbrium properties like thermodynamic potentials do with equilibrium states. In particular, Ω can be used to determine the exact response of particle systems obeying classical mechanical laws, subjected to perturbations of arbitrary size. Under certain conditions, it can also be used to express the response of a single system, in contrast to the standard response theory, which concerns ensembles of identical systems. The dimensions of Ω are those of a rate, hence Ω can be associated with the entropy production rate, provided local thermodynamic equilibrium holds. When this is not the case for a particle system, or generic dynamical systems are considered, Ω can equally be defined, and it yields formal, thermodynamic-like, relations. While such relations may have no physical content, they may still constitute interesting characterizations of the relevant dynamics. Moreover, such a formal approach turns physically relevant, because it allows a deeper analysis of Ω and of response theory than possible in case of fully fledged physical models. Here, we investigate the relation between linear and exact response, pointing out conditions for the validity of the response theory, as well as difficulties and opportunities for the physical interpretation of certain formal results.

On the different formalisms for the transport equations of thermoelectricity: A review

2015 ◽  
Vol 40 (3) ◽  
Author(s):  
José A. Manzanares ◽  
Miikka Jokinen ◽  
Javier Cervera
Keyword(s):  
Entropy Production ◽  
Transport Equations ◽  
Dissipation Function ◽  
Point Of View ◽  
Entropy Production Rate ◽  
Systematic Classification ◽  
Seebeck Coefficients ◽  
Primary Focus

AbstractResearchers in thermoelectricity with backgrounds in non-equilibrium thermodynamics, thermoelectric engineering or condensed-matter physics tend to use different choices of flux densities and generalized forces. These choices are seldom justified from either the dissipation function or the entropy production rate. Because thermoelectric phenomena are a primary focus in several emerging fields, particularly in recent energy-oriented developments, a review of the different formalisms employed is judged timely. A systematic classification of the transport equations is presented here. The requirements on valid transport equations imposed by the invariance of the entropy production are clearly explained. The effective Peltier and Seebeck coefficients, and the thermal conductivity, corresponding to the different choices of flux densities and generalized forces, are identified. Emphasis is made on illustrating the compatibility of apparently disparate formalisms. The advantages and drawbacks of these formalisms are discussed, especially from the point of view of the experimental determination of their thermoelectric coefficients.

scholarly journals Walking droplets through the lens of dynamical systems

2020 ◽  
Vol 34 (34) ◽  
pp. 2030009
Author(s):  
Aminur Rahman ◽  
Denis Blackmore
Keyword(s):  
Nonlinear Dynamics ◽  
Quantum Mechanics ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Systems Analysis ◽  
Research Field ◽  
Physical Models ◽  
The Past ◽  
Dynamical Systems Analysis ◽  
History Of

Over the past decade the study of fluidic droplets bouncing and skipping (or “walking”) on a vibrating fluid bath has gone from an interesting experiment to a vibrant research field. The field exhibits challenging fluids problems, potential connections with quantum mechanics, and complex nonlinear dynamics. We detail advancements in the field of walking droplets through the lens of Dynamical Systems Theory, and outline questions that can be answered using dynamical systems analysis. The paper begins by discussing the history of the fluidic experiments and their resemblance to quantum experiments. With this physics backdrop, we paint a portrait of the complex nonlinear dynamics present in physical models of various walking droplet systems. Naturally, these investigations lead to even more questions, and some unsolved problems that are bound to benefit from rigorous Dynamical Systems Analysis are outlined.

scholarly journals Herd Behavior and Financial Crashes: An Interacting Particle System Approach

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Vincenzo Crescimanna ◽  
Luca Di Persio
Keyword(s):  
Financial Markets ◽  
Private Information ◽  
Particle System ◽  
Physical Models ◽  
Herd Behavior ◽  
Coupling Coefficients ◽  
Market Returns ◽  
Interacting Particle ◽  
The Impact ◽  
With Memory

We provide an approach based on a modification of the Ising model to describe the dynamics of stock markets. Our model incorporates three different factors: imitation, the impact of external news, and private information; moreover, it is characterized by coupling coefficients, static in time, but not identical for each agent. By analogy with physical models, we consider thetemperatureparameter of the system, assuming that it evolves with memory of the past, hence considering how former news influences realized market returns. We show that a standard Ising potential assumption is not sufficient to reproduce the stylized facts characterizing financial markets; this is because it assigns low probabilities to rare events. Hence, we study a variation of the previous setting providing, also by concrete computations, new insights and improvements.

DYNAMICS OF CREMONA MAPS FROM PHYSICAL MODELS

2001 ◽  
Vol 15 (24n25) ◽  
pp. 3279-3286
Author(s):  
W. SCHWALM ◽  
B. MORITZ ◽  
M. SCHWALM
Keyword(s):  
Dynamical Systems ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Physical Models ◽  
Invariant Curves ◽  
Chiral Potts Model ◽  
Cremona Transformation ◽  
Rational Mapping ◽  
Area Preserving Maps ◽  
The Matrix

A Cremona transformation X=f(x, y), Y=g(x, y) is a rational mapping (meaning that f and g are ratios of polynomials) with rational inverse x=F(X, Y), y=G(X, Y). Discrete dynamical systems defined by such transformations are well studied. They include symmetries of the Yang-Baxter equations and their generalizations. In this paper we comment on two types of dynamical systems based on Cremona transformations. The first is the P1 case of Bellon et al. which pertains to the inversion relation for the matrix of Boltzmann weights of the 4-state chiral Potts model. The resulting dynamical system decouples completely to one in a single variable. The sub case z=x corresponds to the symmetric Ashkin-Teller model. We solve this case explicitly giving orbits as closed formulas in the number n of iterations. The second type of system treated is an extension from the famous example due to McMillan of invariant curves of area preserving maps in two dimensions to the case of invariant curves and surfaces of three dimensional Cremona maps that preserve volume. The trace map of the renormalization of transmission through a Fibonacci chain, first introduced by Kohmoto, Kadanoff and Tang, is considered as an example of such a system.

A Note on the Principle of Maximum Dissipation Rate

2006 ◽  
Vol 74 (5) ◽  
pp. 923-926 ◽  
Author(s):  
F. D. Fischer ◽  
J. Svoboda
Keyword(s):  
Convex Functions ◽  
Dissipation Rate ◽  
Direct Consequence ◽  
Dissipation Function ◽  
Internal Variables ◽  
Entropy Production Rate ◽  
Kinetic Rate ◽  
Rate Laws ◽  
Thermodynamic Forces ◽  
Principle Of Maximum

The Principle of Maximum Dissipation Rate (PMD) can be exploited to derive homogeneous kinetic rate laws for the internal variables. A “normality structure” expressing the rates of the internal variables as normal to convex functions (entropy production rate, dissipation function as flow potentials) in the space of the conjugate thermodynamic forces is a direct consequence of the PMD. This paper can be considered as a note to Yang et al., 2005, ASME J. Appl. Mech., 72, pp. 322–329.

scholarly journals Formal Approach to Control Design of Complex and Dynamical Systems

2017 ◽  
Vol 108 ◽  
pp. 2512-2516
Author(s):  
Hela Kadri ◽  
Samir Ben Ahmed ◽  
Simon Collart-Dutilleul
Keyword(s):  
Dynamical Systems ◽  
Control Design ◽  
Formal Approach
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