376 research outputs found
Fluctuation relations for equilibrium states with broken discrete or continuous symmetries
Isometric fluctuation relations are deduced for the fluctuations of the order
parameter in equilibrium systems of condensed-matter physics with broken
discrete or continuous symmetries. These relations are similar to their
analogues obtained for non-equilibrium systems where the broken symmetry is
time reversal. At equilibrium, these relations show that the ratio of the
probabilities of opposite fluctuations goes exponentially with the
symmetry-breaking external field and the magnitude of the fluctuations. These
relations are applied to the Curie-Weiss, Heisenberg, and ~models of
magnetism where the continuous rotational symmetry is broken, as well as to the
-state Potts model and the -state clock model where discrete symmetries
are broken. Broken symmetries are also considered in the anisotropic
Curie-Weiss model. For infinite systems, the results are calculated using
large-deviation theory. The relations are also applied to mean-field models of
nematic liquid crystals where the order parameter is tensorial. Moreover, their
extension to quantum systems is also deduced.Comment: 34 pages, 14 figure
Reaction kinetics in open reactors and serial transfers between closed reactors
Kinetic theory and thermodynamics of reaction networks are extended to the
out-of-equilibrium dynamics of continuous-flow stirred tank reactors (CSTR) and
serial transfers. On the basis of their stoichiometry matrix, the conservation
laws and the cycles of the network are determined for both dynamics. It is
shown that the CSTR and serial transfer dynamics are equivalent in the limit
where the time interval between the transfers tends to zero proportionally to
the ratio of the fractions of fresh to transferred solutions. These results are
illustrated with finite cross-catalytic reaction network and an infinite
reaction network describing mass exchange between polymers. Serial transfer
dynamics is typically used in molecular evolution experiments in the context of
research on the origins of life. The present study is shedding a new light on
the role played by serial transfer parameters in these experiments.Comment: 11 pages, 7 figure
Degree of coupling and efficiency of energy converters far-from-equilibrium
In this paper, we introduce a real symmetric and positive semi-definite
matrix, which we call the non-equilibrium conductance matrix, and which
generalizes the Onsager response matrix for a system in a non-equilibrium
stationary state. We then express the thermodynamic efficiency in terms of the
coefficients of this matrix using a parametrization similar to the one used
near equilibrium. This framework, then valid arbitrarily far from equilibrium
allows to set bounds on the thermodynamic efficiency by a universal function
depending only on the degree of coupling between input and output currents. It
also leads to new general power-efficiency trade-offs valid for macroscopic
machines that are compared to trade-offs previously obtained from uncertainty
relations. We illustrate our results on an unicycle heat to heat converter and
on a discrete model of molecular motor.Comment: 24 pages, 5 figure
A Poisson-Boltzmann approach for a lipid membrane in an electric field
The behavior of a non-conductive quasi-planar lipid membrane in an
electrolyte and in a static (DC) electric field is investigated theoretically
in the nonlinear (Poisson-Boltzmann) regime. Electrostatic effects due to
charges in the membrane lipids and in the double layers lead to corrections to
the membrane elastic moduli which are analyzed here. We show that, especially
in the low salt limit, i) the electrostatic contribution to the membrane's
surface tension due to the Debye layers crosses over from a quadratic behavior
in the externally applied voltage to a linear voltage regime. ii) the
contribution to the membrane's bending modulus due to the Debye layers
saturates for high voltages. Nevertheless, the membrane undulation instability
due to an effectively negative surface tension as predicted by linear
Debye-H\"uckel theory is shown to persist in the nonlinear, high voltage
regime.Comment: 15 pages, 4 figure
Barrier Frank-Wolfe for Marginal Inference
We introduce a globally-convergent algorithm for optimizing the
tree-reweighted (TRW) variational objective over the marginal polytope. The
algorithm is based on the conditional gradient method (Frank-Wolfe) and moves
pseudomarginals within the marginal polytope through repeated maximum a
posteriori (MAP) calls. This modular structure enables us to leverage black-box
MAP solvers (both exact and approximate) for variational inference, and obtains
more accurate results than tree-reweighted algorithms that optimize over the
local consistency relaxation. Theoretically, we bound the sub-optimality for
the proposed algorithm despite the TRW objective having unbounded gradients at
the boundary of the marginal polytope. Empirically, we demonstrate the
increased quality of results found by tightening the relaxation over the
marginal polytope as well as the spanning tree polytope on synthetic and
real-world instances.Comment: 25 pages, 12 figures, To appear in Neural Information Processing
Systems (NIPS) 2015, Corrected reference and cleaned up bibliograph
Inequalities generalizing the second law of thermodynamics for transitions between non-stationary states
We discuss the consequences of a variant of the Hatano-Sasa relation in which
a non-stationary distribution is used in place of the usual stationary one. We
first show that this non-stationary distribution is related to a difference of
traffic between the direct and dual dynamics. With this formalism, we extend
the definition of the adiabatic and non-adiabatic entropies introduced by M.
Esposito and C. Van den Broeck in Phys. Rev. Lett. 104, 090601 (2010) for the
stationary case. We also obtain interesting second-law like inequalities for
transitions between non-stationary states.Comment: 4 pages, 2 figure
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