Phase transitions in “small” systems – A challenge for thermodynamics

Gross, D. H. E.

doi:10.1016/s0375-9474(00)00540-6

Cited by 22 publications

(22 citation statements)

References 28 publications

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“…The surface shows three pronounced maxima and reveals the threefold symmetry of the entropy surface (compare also Fig. 3.25 in [2]). The simulation gives the entropy up to a trivial additive constant.…”

Section: Resultsmentioning

confidence: 76%

“…The three-state Potts model can be investigated analytically within the plaquette approximation [2]. This approach also reveals the three-fold C 3v symmetry of the entropy surface for fixed energies.…”

Section: Three-state Potts Modelmentioning

confidence: 98%

“…As the total number of spins is fixed to be N these numbers are subjected to the subsidiary condition N (1) + N (2) + N (3) = N which defines a plane in the three-dimensional space spanned by the N (σ i ) . The possible macrostates are therefore characterised by the internal energy E and the two numbers N (1) and N (2) of spins in the state 1 and 2, respectively. In this two-dimensional plane the coordinates are chosen in such a way that the completely disordered macrostate (N/3, N/3) where all spin states are equally likely corresponds to the magnetisation (M 1 = 0, M 2 = 0).…”

Section: Three-state Potts Modelmentioning

confidence: 99%

“…Here σ (1) denotes the reflection about the m 1 direction, similarly σ (2) and σ (3) denote the reflection about the symmetry lines defined by the angles 2π/3 and 4π/3. The group C 3v can be decomposed into left cosets with respect to G giving the additional cosets…”

Section: Three-state Potts Modelmentioning

confidence: 99%

“…The starting point of the statistical description is the density of states or equivalently the microcanonical entropy which is usually transformed to the canonical partition function. In recent years the statistical properties of various systems have been deduced directly from the microcanonical entropy [1,2]. In particular first order phase transitions [3,5,4] and critical phenomena have been extensively analysed [6,7].…”

Section: Introductionmentioning

confidence: 99%

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Symmetries of microcanonical entropy surfaces

Behrinǵer¹

2003

J. Phys. A: Math. Gen.

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Abstract. Symmetry properties of the microcanonical entropy surface as a function of the energy and the order parameter are deduced from the invariance group of the Hamiltonian of the physical system. The consequences of these symmetries for the microcanonical order parameter in the high energy and in the low energy phases are investigated. In particular the breaking of the symmetry of the microcanonical entropy in the low energy regime is considered. The general statements are corroborated by investigations of various examples of classical spin systems.

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Section: Resultsmentioning

confidence: 76%

Section: Three-state Potts Modelmentioning

confidence: 98%

Section: Three-state Potts Modelmentioning

confidence: 99%

Section: Three-state Potts Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Symmetries of microcanonical entropy surfaces

Behrinǵer¹

2003

J. Phys. A: Math. Gen.

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Foundations of Thermodynamics

Hardy¹,

Binek²

2014

Thermodynamics and Statistical Mechanics

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Abstract. On the basis of new, concise foundations, this paper establishes the four laws of thermodynamics, the Maxwell relations, and the stability requirements for response functions, in a form applicable to global (homogeneous), local (hydrodynamic) and microlocal (kinetic) equilibrium.The present, self-contained treatment needs very little formal machinery and stays very close to the formulas as they are applied by the practicing physicist, chemist, or engineer. From a few basic assumptions, the full structure of phenomenological thermodynamics and of classical and quantum statistical mechanics is recovered.Care has been taken to keep the foundations free of subjective aspects (which traditionally creep in through information or probability). One might describe the paper as a uniform treatment of the nondynamical part of classical and quantum statistical mechanics "without statistics" (i.e., suitable for the definite descriptions of single objects) and "without mechanics" (i.e., independent of microscopic assumptions). When enriched by the traditional examples and applications, this paper may serve as the basis for a course on thermal physics.

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Thermo-statistics or Topology of the Microcanonical Entropy Surface

Gross

2002

Dynamics and Thermodynamics of Systems With Long-Range Interactions

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Boltzmann's principle S(E, N, V · · · ) = ln W (E, N, V · · · ) allows the interpretation of Statistical Mechanics of a closed system as Pseudo-Riemannian geometry in the space of the conserved parameters E, N, V · · · (the conserved mechanical parameters in the language of Ruppeiner [1]) without invoking the thermodynamic limit. The topology is controlled by the curvature of S(E, N, V · · · ). The most interesting region is the region of (wrong) positive maximum curvature, the region of phase-separation. This is demonstrated among others for the equilibrium of a typical non-extensive system, a self-gravitating and rotating cloud in a spherical container at various energies and angular-momenta. A rich variety of realistic configurations, as single stars, multistar systems, rings and finally gas, are obtained as equilibrium microcanonical phases. The global phase diagram, the topology of the curvature, as function of energy and angular-momentum is presented. No exotic form of thermodynamics like Tsallis [2,3] non-extensive one is necessary. It is further shown that a finite (even mesoscopic) system approaches equilibrium with a change of its entropy ∆S ≥ 0 (Second Law) even when its Poincarré recurrence time is not large.

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Phase transitions in “small” systems – A challenge for thermodynamics

Cited by 22 publications

References 28 publications

Symmetries of microcanonical entropy surfaces

Symmetries of microcanonical entropy surfaces

Foundations of Thermodynamics

Thermo-statistics or Topology of the Microcanonical Entropy Surface

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