Evolution of dissipative processes via a statistical thermodynamic approach. I. Generalized Mori–Heisenberg–Langevin equations

Madureira, Justino R.; Vasconcellos, Áurea R.; Luzzi, Roberto; Casas-Vázquez, José; Jou, David

doi:10.1063/1.476191

Cited by 37 publications

(7 citation statements)

References 16 publications

(33 reference statements)

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“…22 It is shown that the higherorder fluxes keep dying down as time elapses and then we can retain less and less higher-order fluxes in the description of the movement. 20 This is related to Bogoliubov's hierarchy of relaxation times, 23 which, for the case of semiconductors, is described in Refs. 14, 24, and 25.…”

Section: ͑31͒mentioning

confidence: 99%

Thermoelastic analysis of a silicon surface under x-ray free-electron-laser irradiation

Castro

Vasconcellos

Luzzi

2010

Review of Scientific Instruments

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We present an analysis of the time evolution of a highly excited silicon substrate after partial absorption of a femtosecond soft x-ray pulse. The detailed time-dependent thermoelastic behavior of the substrate in terms of the displacements u(r,t) is derived for time delays for which the usual local thermodynamic variables, temperature T(r,t) and density n(r,t), become well-defined, namely, a few hundred femtoseconds after x-ray pulse absorption. For practical optical components under present conditions of operation with trains of pulses, we find that in a worst case scenario, already the 50th pulse in the train could be adversely affected by dynamic distortion induced by the preceding pulses [corrected]

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Section: ͑31͒mentioning

confidence: 99%

Thermoelastic analysis of a silicon surface under x-ray free-electron-laser irradiation

Castro

Vasconcellos

Luzzi

2010

Review of Scientific Instruments

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“…Remark 2.9. Indeed, according to information theory, the entropy flux has the form of the sum of several fluxes, each of them multiplied by the thermodynamic conjugate variable of the quantity transported by the flux (such conjugate variable is given by the derivative of the entropy with respect to the variable) [27][28][29]. Note that this is satisfied by the particular expression in equation (2.35).…”

Section: Compatibility With Second Law Of Thermodynamicsmentioning

confidence: 99%

Differential consequences of balance laws in extended irreversible thermodynamics of rigid heat conductors

Rogolino

Cimmelli

2019

Proc. R. Soc. A.

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We consider a system of balance laws arising in extended irreversible thermodynamics of rigid heat conductors, together with its differential consequences, namely the higher-order system obtained by taking into account the time and space derivatives of the original system. We point out some mathematical properties of the differential consequences, with particular attention to the problem of the propagation of thermal perturbations with finite speed. We prove that, under an opportune choice of the initial conditions, a solution of the Cauchy problem for the system of differential consequences is also a solution of the Cauchy problem for the original system. We investigate the thermodynamic compatibility of the system at hand by applying a generalized Coleman-Noll procedure. On the example of a generalized Guyer-Krumhansl heat-transport model, we show that it is possible to get a hyperbolic system of evolution equations even when the state space is non-local.

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“…Lauck, Vasconcellos and Luzzi [27] developed a nonlinear quantum transport theory for a far from equilibrium many-body system, which is based on nonequilibrium statistical operator method. The hierarchy of generalized evolution equations of dissipative processes in a Bose fluid was derived by Madureira, Vasconcellos and Luzzi [28,29]. The proposed approach may be suitable for a description of the transport coefficients in molecular hydrodynamics, where the coefficients are frequency and wavelength dependent.…”

Section: Introductionmentioning

confidence: 99%

Quantum transport equations for Bose systems taking into account nonlinear hydrodynamic processes

Hlushak¹,

Токарчук²

2014

Condens. Matter Phys.

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Using the method of nonequilibrium statistical operator by Zubarev, an approach is proposed for the description of kinetics which takes into account the nonlinear hydrodynamic fluctuations for a quantum Bose system. Non-equilibrium statistical operator is presented which consistently describes both the kinetic and nonlinear hydrodynamic processes. Both a kinetic equation for the nonequilibrium one-particle distribution function and a generalized Fokker-Planck equation for nonequilibrium distribution function of hydrodynamic variables (densities of momentum, energy and particle number) are obtained. A structure function of hydrodynamic fluctuations in cumulant representation is calculated, which makes it possible to analyse the generalized Fokker-Planck equation in Gaussian and higher approximations of the dynamic correlations of hydrodynamic variables which is important in describing the quantum turbulent processes.

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Evolution of dissipative processes via a statistical thermodynamic approach. I. Generalized Mori–Heisenberg–Langevin equations

Cited by 37 publications

References 16 publications

Thermoelastic analysis of a silicon surface under x-ray free-electron-laser irradiation

Thermoelastic analysis of a silicon surface under x-ray free-electron-laser irradiation

Differential consequences of balance laws in extended irreversible thermodynamics of rigid heat conductors

Quantum transport equations for Bose systems taking into account nonlinear hydrodynamic processes

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