Galilean relativistic fluid mechanics

Ván, P.

doi:10.1007/s00161-016-0545-7

Cited by 14 publications

(14 citation statements)

References 83 publications

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“…frame-independent, treatment requires a four-dimensional space-time representation of the physical quantities also in a non-relativistic case. In this work, we consider the following aspects of a more rigorous nonrelativistic formalism [18,19]:…”

Section: Gradients and Internal Variables In Nonequilibrium Thermodynmentioning

confidence: 99%

Variational principles and nonequilibrium thermodynamics

Ván

Kovács

2020

Phil. Trans. R. Soc. A.

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Variational principles play a fundamental role in deriving the evolution equations of physics. They work well in the case of non-dissipative evolution, but for dissipative systems, the variational principles are not unique and not constructive. With the methods of modern nonequilibrium thermodynamics, one can derive evolution equations for dissipative phenomena and, surprisingly, in several cases, one can also reproduce the Euler–Lagrange form and symplectic structure of the evolution equations for non-dissipative processes. In this work, we examine some demonstrative examples and compare thermodynamic and variational techniques. Then, we argue that, instead of searching for variational principles for dissipative systems, there is another viable programme: the second law alone can be an effective tool to construct evolution equations for both dissipative and non-dissipative processes. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

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Section: Gradients and Internal Variables In Nonequilibrium Thermodynmentioning

confidence: 99%

Variational principles and nonequilibrium thermodynamics

Ván

Kovács

2020

Phil. Trans. R. Soc. A.

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“…Our strategy is based on a variational approach. In particular, we search for such histories that extremize the irreversible work loss δW gas = 0 for 14) which is merely the integral of equation (2.9). Note, that for isothermal workv z is a history independent constant.…”

Section: (B) Work and The Equation Of Statesmentioning

confidence: 99%

“…On the other hand, for systems working between an energy potential, e.g. a hot and a cold reservoir, which drives a continuous energy current through the system, the local equilibrium assumption is typically violated, and often one has to resort to numerical simulations as the primary (and often the only) diagnostic tool [12,13], despite recent advances in the theory of driven systems [14,15].…”

Section: Introductionmentioning

confidence: 99%

Time–energy uncertainty principle for irreversible heat engines

Hanel

Jizba

2020

Phil. Trans. R. Soc. A.

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Even though irreversibility is one of the major hallmarks of any real-life process, an actual understanding of irreversible processes remains still mostly semi-empirical. In this paper, we formulate a thermodynamic uncertainty principle for irreversible heat engines operating with an ideal gas as a working medium. In particular, we show that the time needed to run through such an irreversible cycle multiplied by the irreversible work lost in the cycle is bounded from below by an irreducible and process-dependent constant that has the dimension of an action. The constant in question depends on a typical scale of the process and becomes comparable to Planck’s constant at the length scale of the order Bohr radius, i.e. the scale that corresponds to the smallest distance on which the ideal gas paradigm realistically applies. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

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“…First, it is the invariance with respect to the Galilean transformations. Consequences of the requirement of the Galilean invariance have been investigated very systematically in [1], [52] and more recently and in a somewhat different mathematical setting in [53], [41]. The second structure is related to the regularity of solutions, in particular then to the wave propagation and the existence of shock waves (see [1], [54], [4], [55], [24]).…”

Section: Other Mathematical Structuresmentioning

confidence: 99%

Hamiltonian and Godunov structures of the Grad hierarchy

et al. 2017

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The time evolution governed by the Boltzmann kinetic equation is compatible with mechanics and thermodynamics. The former compatibility is mathematically expressed in the Hamiltonian and Godunov structures, the latter in the structure of gradient dynamics guaranteeing the growth of entropy and consequently the approach to equilibrium. We carry all three structures to the Grad reformulation of the Boltzmann equation (to the Grad hierarchy). First, we recognize the structures in the infinite Grad hierarchy and then in several examples of finite hierarchies representing extended hydrodynamic equations. In the context of Grad's hierarchies we also investigate relations between Hamiltonian and Godunov structures.

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Galilean relativistic fluid mechanics

Cited by 14 publications

References 83 publications

Variational principles and nonequilibrium thermodynamics

Variational principles and nonequilibrium thermodynamics

Time–energy uncertainty principle for irreversible heat engines

Hamiltonian and Godunov structures of the Grad hierarchy

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