Nonlinear Phenomena in Complex Systems, 2001, Vol.4, No.4, pp.318-321

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2001, Volume 4, Number 4, pp.318-321

Thermodynamics and Spectral Radius
A. Antonevich, V. Bakhtin, and A. Lebedev

The formula for the spectral radius of arbitrary weighted shift operators acting in L^p spaces is established. The formula contains as a component a new dynamical invariant - T-entropy (a mathematical analogue to the thermodynamic entropy). It is proved that the logarithm of the spectral radius and the T-entropy are linked by the Legendre transform.
Key words: T-entropy, weighted shift operator, Legendre transform, spectral radius

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