Thermodynamic formalism and linear response theory for non-equilibrium steady states

Abstract

The accurate determination of transport coefficients in numerical simulations is becoming increasingly important in a wide range of applications. Here we consider the linear response in systems driven away from thermal equilibrium into a non-equilibrium steady state with non-vanishing entropy production rate. A simple derivation of a general response formula is presented. For Markov processes we explicitly construct the conjugate quantities and discuss their relation with known response formulas. Emphasis is put on the formal analogy with thermodynamic potentials and some consequences are discussed.

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• Modeling of biomolecular machines in non-equilibrium steady states
• Thermodynamic formalism for transport coefficients with an application to the shear modulus and shear viscosity
• Macroscopic fluctuation-response theory and its use for gene regulatory networks
• Estimating linear response statistics using orthogonal polynomials: An RKHS formulation