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Uniform treatment of fluctuations at critical points

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  • Mangel, Marc

Abstract

A generalized critical point is characterized by the vanishing of certain linear relationships. In particular, the dynamics near such a point are non-linear. In this paper, we study fluctuations at such points of spatially homogeneous systems. We discuss thermodynamic critical points as a special case; but the main emphasis is on stochastic kinetic equations. We show that fluctuations at a critical point cannot be characterized by a Gaussian density, but more complicated densities can be used. The theory is applied to the critical harmonic oscillator.

Suggested Citation

  • Mangel, Marc, 1979. "Uniform treatment of fluctuations at critical points," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 97(3), pages 597-615.
    • Handle: RePEc:eee:phsmap:v:97:y:1979:i:3:p:597-615
    DOI: 10.1016/0378-4371(79)90099-2
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    References listed on IDEAS

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    1. Rodríguez, R.F. & Van Kampen, N.G., 1976. "Systematic treatment of fluctuations in a nonlinear oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 85(2), pages 347-362.
    2. Chapman, Duane & Mount, Timothy & Tyrrell, Timothy J., 1972. "Predicting the Past and Future in Electricity Demand," Staff Papers 185924, Cornell University, Department of Applied Economics and Management.
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