Extended Irreversible Thermodynamics

Jou, David; Casas-Vázquez, José; Lebon, Georgy

doi:10.1007/978-3-642-97671-1_2

Cited by 71 publications

(124 citation statements)

References 33 publications

Supporting

Mentioning

124

Contrasting

Order By: Relevance

“…ðA À A n Þ is also one to one. On the other hand, Equation (4), in Assumption A2, imposes a relationship between diffusive fluxes and thermodynamic forces X (the spatial gradients of A) known in irreversible thermodynamics as the Onsager-Casimir relationships (see, for instance Reference [2,19]). Finally, SðzÞ in (2) is assumed to be Lipschitz continuous.…”

Section: Dissipative Systems: Description and Propertiesmentioning

confidence: 99%

“…Vector functions f k ; SðzÞ and p describe microscopic fluxes through the domain, production densities and controls, respectively. Fluxes and production terms in dissipative systems have a particular structure, well motivated by thermodynamic arguments [19]. In this way, the flux vector f k can be partitioned into convective and diffusive contributions as follows: (4) is assumed to be positive definite and symmetric.…”

Section: Dissipative Systems: Description and Propertiesmentioning

confidence: 99%

See 1 more Smart Citation

Dissipative systems: from physics to robust nonlinear control

Alonso¹,

Vilas²,

Banga³

2003

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

SUMMARYIn this paper, we explore connections between the underlying physics of dissipative systems and nonlinear robust control. In particular, we concentrate on the problem of stabilizing stationary solutions of nonlinear dissipative systems with states distributed in space. Dissipative systems are equipped with an entropy function which we employ to relate dissipation with the Hamilton-Jacobi-Bellman equation. This relation allows us to establish formal links between the dynamic properties of dissipative systems, passivity and optimal stabilizing control, as it is understood in systems theory. Robustness issues in controller design, are also discussed in the context of front or pulse spatial pattern stabilization.

show abstract

Section: Dissipative Systems: Description and Propertiesmentioning

confidence: 99%

Section: Dissipative Systems: Description and Propertiesmentioning

confidence: 99%

Dissipative systems: from physics to robust nonlinear control

Alonso¹,

Vilas²,

Banga³

2003

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…The description of the conductor linking the system and the thermometer alters T LTE . In the implementation by Jou et al [3][4][5][6], the forced oscillator may bring the second oscillator out of equilibrium and for the forcing frequency different from the system frequency, T C = T K . Under such conditions, the basic tenets of the local thermodynamic equilibrium are violated as the existence of T LTE implies T C = T K .…”

Section: Previous Efforts In Determining Nonequilibrium Temperaturementioning

confidence: 99%

“…Temperature is one such variable of interest [4]. Defining temperature and its measurement using thermometers relies upon the validity of the Zeroth Law of thermodynamics [5]-the mutual thermal equilibrium of three contacting bodies.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium temperature measurement in a thermal conduction process

Patra

Batra

2017

Phys. Rev. E

View full text Add to dashboard Cite

We identify the temperature being measured by a thermometer in a nonequilibrium scenario by studying heat conduction in a three-dimensional Lennard-Jones (LJ) system whose two ends are kept at different temperatures. It is accomplished by modeling the thermometer particles also with the LJ potential but with added tethers to prevent their rigid body motion. These models of the system and the thermometer mimic a real scenario in which a mechanical thermometer is "inserted" into a system and kept there long enough for the temperature to reach a steady value. The system is divided into five strips, and for each strip the temperature is measured using an embedded thermometer. Unlike previous works, these thermometers are small enough not to alter the steady state of the nonequilibrium system. After showing initial transients, the thermometers eventually show steady-state conditions with the subregions of the system and provide values of the different temperature definitions-kinetic, configurational, dynamical, and higher-order configurational. It is found that their kinetic and the configurational temperatures are close to the system's kinetic temperature except in the two thermostatted regions. In the thermostatted regions, where the system's kinetic and the configurational temperatures are significantly different, the thermometers register a temperature substantially different from either of these two values. With a decrease in the system density and size, these differences between the kinetic and the configurational temperatures of the thermometer become more pronounced.

show abstract

“…Another important difference between this and earlier work is that, instead of the Israel -Stewart [41][42][43] framework (or similar frameworks, such as "Extended Thermodynamics" [44]) , we shall work within the class of "Divergence Type Theories" (DTT) earlier introduced by Geroch [1]. DTTs are appealing because they represent a mathematically consistent, closed system, rather than a truncated expansion in deviations from ideal behavior.…”

mentioning

confidence: 99%

Relativistic theories of interacting fields and fluids

Calzetta¹,

Thibeault²

2001

Phys. Rev. D

View full text Add to dashboard Cite

We investigate divergence-type theories describing the disipative interaction betwen a field and a fluid. We look for theories which, under equilibrium conditions, reduce to the theory of a Klein-Gordon scalar field and a perfect fluid. We show that the requirements of causality and positivity of entropy production put non-trivial constraints to the structure of the interaction terms. These theories provide a basis for the phenomonological study of the reheating period.

show abstract

Extended Irreversible Thermodynamics

Cited by 71 publications

References 33 publications

Dissipative systems: from physics to robust nonlinear control

Dissipative systems: from physics to robust nonlinear control

Nonequilibrium temperature measurement in a thermal conduction process

Relativistic theories of interacting fields and fluids

Contact Info

Product

Resources

About