The hidden fluctuation-dissipation theorem for growth

Abstract

In a stochastic process, where noise is always present, the fluctuation-dissipation theorem (FDT) becomes one of the most important tools in statistical mechanics and, consequently, it appears everywhere. Its major utility is to provide a simple response to study certain processes in solids and fluids. However, in many situations we are not talking about a FDT, but about the noise intensity. For example, noise has enormous importance in diffusion and growth phenomena. Although we have an explicit FDT for diffusion phenomena, we do not have one for growth processes where we have a noise intensity. We show that there is a hidden FDT for the growth phenomenon, similar to the diffusive one. Moreover, we show that growth with correlated noise presents as well a similar form of FDT. We also call attention to the hierarchy within the theorems of statistical mechanics and how this explains the violation of the FDT in some phenomena.

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Cited by in corpus (9)

• The Kardar-Parisi-Zhang exponents for the $2+1$ dimensions
• The fractal geometry of growth: fluctuation-dissipation theorem and hidden symmetry
• The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
• Universal scaling relation for growth phenomena
• Restoring the fluctuation-dissipation theorem in Kardar-Parisi-Zhang universality class through a new emergent fractal dimension
• A geometrical interpretation of critical exponents
• Random Walk on a Random Surface: Implications of Non-perturbative Concepts and Dynamical Emergence of Galilean Symmetry
• Fractality in resistive circuits: The Fibonacci resistor networks
• Scaling, Fractal Dynamics and Critical Exponents: Application in a non-integer dimensional Ising model