Considerations on nonequilibrium entropy and temperature

Ramos, J. Galvão; Vasconcellos, Áurea R.; Luzzi, Roberto

doi:10.1590/s0103-97332000000300021

Cited by 4 publications

(5 citation statements)

References 59 publications

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Section: Applicationsmentioning

confidence: 91%

“…Thus, even though Onsager relations are satisfied, the coefficient's dependence on nonequilibrium state variables and external fields, indicates that any variational principle associated with the entropy production [132,134,135,140,141], is not applicable to the present case [69,142] In the absence of the BGK reactive term, null magnetic field, and for the strictly stationary inhomogeneous bath case, we recover the inhomogeneous media advection-diffusion equation, presented by [96] and given by ∂n(x,t) ∂t = ∇ (λ(x) [n(x,t)∇U (x) + n(x,t)∇T (x) + T (x)∇n(x,t)]) (62) and for the rigid conductor (constant particle density n), no reactive term and null external fields, we retrieve the inertial corrections to Fourier's law, known as the Maxwell-Cattaneo equation [137]- [139] (of the hyperbolic type, known also as the telegrapher's equation)…”

Section: : Applicationsmentioning

confidence: 99%

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Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

Lagos

Simões

2011

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tWe consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski-reactive like equation; for the particle's momentum density, a generalized Ohm's-like equation; and for the particle's energy density, a Maxwell-Cattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles.

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Section: Applicationsmentioning

confidence: 91%

Section: : Applicationsmentioning

confidence: 99%

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

Lagos

Simões

2011

Physica A: Statistical Mechanics and its Applications

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“…Information theory is another field where the question concerning absolute temperature arises in a natural way. Informational statistical thermodynamics (IST) introduces a state function referred to as the informational-statistical entropy, which depends on the basic whole set of macro-variables chosen for the description of the macroscopic state of the system (Grandy 1980, Luzzi and Vasconcellos 1990, Ramos et al 2000, Luzzi et al 2001. This is the generalization of the entropy function of equilibrium thermodynamics and classical irreversible thermodynamics, the expressions of which are recovered in the appropriate limit.…”

Section: Information Theory: Equilibrium Ensemblesmentioning

confidence: 99%

Temperature in non-equilibrium states: a review of open problems and current proposals

2003

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The conceptual problems arising in the definition and measurement of temperature in nonequilibrium states are discussed in this paper in situations where the local-equilibrium hypothesis is no longer satisfactory. This is a necessary and urgent discussion because of the increasing interest in thermodynamic theories beyond local equilibrium, in computer simulations, in non-linear statistical mechanics, in new experiments, and in technological applications of nanoscale systems and material sciences. First, we briefly review the concept of temperature from the perspectives of equilibrium thermodynamics and statistical mechanics. Afterwards, we explore which of the equilibrium concepts may be extrapolated beyond local equilibrium and which of them should be modified, then we review several attempts to define temperature in non-equilibrium situations from macroscopic and microscopic bases. A wide review of proposals is offered on effective non-equilibrium temperatures and their application to ideal and real gases, electromagnetic radiation, nuclear collisions, granular systems, glasses, sheared fluids, amorphous semiconductors and turbulent fluids. The consistency between the different relativistic transformation laws for temperature is discussed in the new light gained from this perspective. A wide bibliography is provided in order to foster further research in this field.

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“…Up to date, however, we have no generally accepted theory for the description of processes far away from equilibrium. But there is a number of promising different approaches like the extended thermodynamics 1 , the nonextensive thermodynamics 2 and the nonequilibrium statistical operator method 3 . Complementary, a number of statistical schemes have been proposed 4,5,6 all based on the projection-operator method.…”

Section: Introduction -Temperature Conceptmentioning

confidence: 99%

The change of thermal properties under the exposure to fs-laser pulses

Huettner¹

2004

High-Power Laser Ablation V

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We start with a short introduction of some newer thermodynamical approaches to the description of nonequilibrium processes related to the interaction of short laser pulses with matter. Then we shall use the example of electronic thermal conductivity to show why the equations usually derived in standard solid state theory have to be reconsidered. This is mandated by the loss of local thermal equilibrium, the nonstationarity, and the enhanced contribution from electronelectron scattering. Based on Boltzmann's equation we derive an expression for the thermal conductivity with new qualitative and quantitative properties. These results are supported by comparison with experiments.

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Considerations on nonequilibrium entropy and temperature

Cited by 4 publications

References 59 publications

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

Temperature in non-equilibrium states: a review of open problems and current proposals

The change of thermal properties under the exposure to fs-laser pulses

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