4,900 research outputs found

### Differentiating the absolutely continuous invariant measure of an interval map f with respect to f

Let the map $f:[-1,1]\to[-1,1]$ have a.c.i.m. $\rho$ (absolutely continuous
$f$-invariant measure with respect to Lebesgue). Let $\delta\rho$ be the change
of $\rho$ corresponding to a perturbation $X=\delta f\circ f^{-1}$ of $f$.
Formally we have, for differentiable $A$, $\delta\rho(A)=\sum_{n=0}^\infty\int\rho(dx) X(x){d\over dx}A(f^nx)$ but this
expression does not converge in general. For $f$ real-analytic and Markovian in
the sense of covering $(-1,1)$ $m$ times, and assuming an {\it analytic
expanding} condition, we show that
$\lambda\mapsto\Psi(\lambda)=\sum_{n=0}^\infty\lambda^n \int\rho(dx)
X(x){d\over dx}A(f^nx)$ is meromorphic in ${\bf C}$, and has no pole at
$\lambda=1$. We can thus formally write $\delta\rho(A)=\Psi(1)$.Comment: 10 pages, plain Te

### Kramers-Wannier dualities via symmetries

Kramers-Wannier dualities in lattice models are intimately connected with
symmetries. We show that they can be found directly and explicitly from the
symmetry transformations of the boundary states in the underlying conformal
field theory. Intriguingly the only models with a self-duality transformation
turn out to be those with an auto-orbifold property.Comment: 4 pages, no figur

### Entropy production in quantum spin systems

We consider a quantum spin system consisting of a finite subsystem connected
to infinite reservoirs at different temperatures. In this setup we define
nonequilibrium steady states and prove that the rate of entropy production in
such states is nonnegative.Comment: In honor of J.L. Lebowit

### How should one define entropy production for nonequilibrium quantum spin systems?

This paper discusses entropy production in nonequilibrium steady states for
infinite quantum spin systems. Rigorous results have been obtained recently in
this area, but a physical discussion shows that some questions of principle
remain to be clarified.Comment: 8 page

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