83,194 research outputs found
Geometrical Phase Transitions
The geometrical approach to phase transitions is illustrated by simulating
the high-temperature representation of the Ising model on a square lattice.Comment: 5 pages, 3 figures, talk presented at Conference on Computational
Physics 2004, Genoa, 1-4 September 2004; 2nd version: slightly expanded
versio
Topological aspects of geometrical signatures of phase transitions
Certain geometric properties of submanifolds of configuration space are
numerically investigated for classical lattice phi^4 models in one and two
dimensions. Peculiar behaviors of the computed geometric quantities are found
only in the two-dimensional case, when a phase transition is present. The
observed phenomenology strongly supports, though in an indirect way, a recently
proposed topological conjecture about a topology change of the configuration
space submanifolds as counterpart of a phase transition.Comment: REVTEX file, 4 pages, 5 figure
Geometrical aspects in the analysis of microcanonical phase-transitions
In the present work, we discuss how the functional form of thermodynamic
observables can be deduced from the geometric properties of subsets of phase
space. The geometric quantities taken into account are mainly extrinsic
curvatures of the energy level sets of the Hamiltonian of a system under
investigation. In particular, it turns out that peculiar behaviours of
thermodynamic observables at a phase transition point are rooted in more
fundamental changes of the geometry of the energy level sets in phase space.
More specifically, we discuss how microcanonical and geometrical descriptions
of phase-transitions are shaped in the special case of models with
either nearest-neighbours and mean-field interactions
Geometrical Expression of Excess Entropy Production
We derive a geometrical expression of the excess entropy production for
quasi-static transitions between nonequilibrium steady states of Markovian jump
processes, which can be exactly applied to nonlinear and nonequilibrium
situations. The obtained expression is geometrical; the excess entropy
production depends only on a trajectory in the parameter space, analogous to
the Berry phase in quantum mechanics. Our results imply that vector potentials
are needed to construct thermodynamics of nonequilibrium steady states
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