Statistical Ensemble Inequivalence and Bicritical Points for Two-Dimensional Flows and Geophysical Flows

Venaille, Antoine; Bouchet, Freddy

doi:10.1103/physrevlett.102.104501

Cited by 76 publications

(112 citation statements)

References 16 publications

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“…When lowering the temperature at fixed K the system first go through a disorder/order transition and then again through an order/disorder one and is, counter intuitively, disordered down to zero temperature. An alternative interpretation of this phenomenon makes reference to azeotropy [26,27]. The two transitions can be of first or second order depending on the chosen value of B.…”

Section: Discussionmentioning

confidence: 99%

Models with short- and long-range interactions: the phase diagram and the reentrant phase

Dauxois¹,

Buyl²,

Lori³

et al. 2010

J. Stat. Mech.

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Abstract. We study the phase diagram of two different Hamiltonians with competiting local, nearest-neighbour, and mean-field couplings. The first example corresponds to the HMF Hamiltonian with an additional short-range interaction. The second example is a reduced Hamiltonian for dipolar layered spin structures, with a new feature with respect to the first example, the presence of anisotropies.The two examples are solved in both the canonical and the microcanonical ensemble using a combination of the min-max method with the transfer operator method. The phase diagrams present typical features of systems with long-range interactions: ensemble inequivalence, negative specific heat and temperature jumps.Moreover, in a given range of parameters, we report the signature of phase reentrance. This can also be interpreted as the presence of azeotropy with the creation of two first order phase transitions with ensemble inequivalence, as one parameter is varied continuously.

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Section: Discussionmentioning

confidence: 99%

Models with short- and long-range interactions: the phase diagram and the reentrant phase

Dauxois¹,

Buyl²,

Lori³

et al. 2010

J. Stat. Mech.

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“…Для классических систем каноническая мера является хорошей аппроксимацией к микроканонической [19], однако для гидродинамических систем это не так, и в работе [39] показана неэквивалент-ность микроканонического и канонического ансамблей.…”

Section: спектральная теория крайчнанаunclassified

Equilibrium states of finite-dimensional approximations of a two-dimensional incompressible inviscid fluid

Perezhogin¹,

Dymnikov²

2017

Nelin. Dinam.

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“…This is at the origin of ensemble inequivalence, which in turn instigates peculiar thermodynamic properties, like negative specific heat and temperature jumps in the microcanonical ensemble. Ensemble inequivalence has been reported to occur in the past for gravitational systems [8], spin models [9] and twodimensional flows [10]. These are extremely interesting models per se, as well as for their theoretical implications, but in general they do not allow for a straightforward experimental verification of the predictions drawn.…”

mentioning

confidence: 99%

“…It is straightforward to see that T mc = γ −1 , where γ is defined by Eq. (10). From a direct inspection of Fig.…”

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confidence: 99%

Ensemble inequivalence in systems with wave-particle interaction

2014

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The classical wave-particle Hamiltonian is considered in its generalized version, where two modes are assumed to interact with the co-evolving charged particles. The equilibrium statistical mechanics solution of the model is worked out analytically, both in the canonical and the microcanonical ensembles. The competition between the two modes is shown to yield ensemble inequivalence, at variance with the standard scenario where just one wave is allowed to develop. As a consequence, both temperature jumps and negative specific heat can show up in the microcanonical ensemble. The relevance of these findings for both plasma physics and Free Electron Laser applications is discussed. [6]. For these systems energy is non additive implying that entropy could be non concave in some range of values of macroscopic extensive parameters [7]. This is at the origin of ensemble inequivalence, which in turn instigates peculiar thermodynamic properties, like negative specific heat and temperature jumps in the microcanonical ensemble. Ensemble inequivalence has been reported to occur in the past for gravitational systems [8], spin models [9] and twodimensional flows [10]. These are extremely interesting models per se, as well as for their theoretical implications, but in general they do not allow for a straightforward experimental verification of the predictions drawn.A paradigmatic example of long range interacting system is represented by the so called wave-particle Hamiltonian, which describes the self-consistent interaction of N charged particles with a co-evolving wave [11]. This is a rather general descriptive scenario, often invoked in different fields of investigations where the mutual coupling between particles and waves proves central, as e.g. in plasma physics [12] and the Free Electron Laser (FEL) [13]. The equilibrium statistical mechanics solution of the celebrated wave-particle Hamiltonian has been so far solely carried out for the simple setting where just one isolated wave is allowed to exist [14,15]. Working under this limiting, and in many respects, unrealistic assumption, it can be shown that the canonical and microcanonical solutions coincide [16]. In real experiments, however, several modes are simultaneously present and interact with the bunch of co-evolving particles. Motivated by this observation and to eventually bridge the gap between theory and experiments, we here consider the generalized equilibrium solution of the reference wave-particle Hamiltonian when a second harmonic is allowed to self-consistently develop. As we shall analytically demonstrate, the insertion of an additional wave causes the ensemble inequivalence to rise, within a specific range of the coupling constants which yield a first order phase transition in the canonical ensemble. This conclusion is reached for a model of marked experimental value, paving the way to direct verifications and, possibly, exploitations of the general concept of ensemble inequivalence.The starting point of our discussion is the universal wave particle Hamil...

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Statistical Ensemble Inequivalence and Bicritical Points for Two-Dimensional Flows and Geophysical Flows

Cited by 76 publications

References 16 publications

Models with short- and long-range interactions: the phase diagram and the reentrant phase

Models with short- and long-range interactions: the phase diagram and the reentrant phase

Equilibrium states of finite-dimensional approximations of a two-dimensional incompressible inviscid fluid

Ensemble inequivalence in systems with wave-particle interaction

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