Tensor Products and Singularly Continuous Spectrum

White, Denis A. W.

doi:10.4153/cmb-1984-076-6

Can. math. bull.

1984

DOI: 10.4153/cmb-1984-076-6

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Tensor Products and Singularly Continuous Spectrum

Denis A. W. White

Abstract: An example of a bounded self adjoint operator A is constructed so that A⊗I + α(I⊗A) is purely singularly continuous but A⊗1 + β(I⊗A) is purely absolutely continuous, for some real α and β. In fact α - β can be chosen arbitrarily small.

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2012

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“…has been a source of dismay [17][18][19], for it is not invariant under a change of variables. In fact, letting…”

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confidence: 99%

Nonequilibrium thermodynamics as a gauge theory

Polettini

2012

EPL

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Abstract. -We assume that markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential. A widely accepted expression for the total entropy production of a system arises as the simplest gauge-invariant completion of the time derivative of Gibbs's entropy. We show that transition rates can be given a simple physical characterization in terms of locally-detailed-balanced heat reservoirs. It follows that Clausius's measure of irreversibility along a cyclic transformation is a geometric phase. In this picture, the gauge symmetry arises as the arbitrariness in the choice of a prior probability. Thermostatics depends on the information that is disposable to an observer; thermodynamics does not.

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“…has been a source of dismay [17][18][19], for it is not invariant under a change of variables. In fact, letting…”

mentioning

confidence: 99%

Nonequilibrium thermodynamics as a gauge theory

Polettini

2012

EPL

View full text Add to dashboard Cite

show abstract

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Tensor Products and Singularly Continuous Spectrum

Abstract: An example of a bounded self adjoint operator A is constructed so that A⊗I + α(I⊗A) is purely singularly continuous but A⊗1 + β(I⊗A) is purely absolutely continuous, for some real α and β. In fact α - β can be chosen arbitrarily small.

Cited by 1 publication

References 7 publications

Nonequilibrium thermodynamics as a gauge theory

Nonequilibrium thermodynamics as a gauge theory

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