General criterion for harmonicity

Proesmans, Karel ; Vandebroek, Hans ; Van Den Broeck, Christian (2017)

CITATION: Proesmans, K., Vandebroek, H. & Van Den Broeck, C. 2017. General criterion for harmonicity. Physical Review Letters, 119(14):1-5, doi:10.1103/PhysRevLett.119.147803.

The original publication is available at https://journals.aps.org/prl

Article

Inspired by Kubo-Anderson Markov processes, we introduce a new class of transfer matrices whose largest eigenvalue is determined by a simple explicit algebraic equation. Applications include the free energy calculation for various equilibrium systems and a general criterion for perfect harmonicity, i.e., a free energy that is exactly quadratic in the external field. As an illustration, we construct a “perfect spring,” namely, a polymer with non-Gaussian, exponentially distributed subunits which, nevertheless, remains harmonic until it is fully stretched. This surprising discovery is confirmed by Monte Carlo and Langevin simulations.

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