Stochastic thermodynamics of fluctuating density fields: Non-equilibrium free energy differences under coarse-graining

Abstract

We discuss the stochastic thermodynamics of systems that are described by a time-dependent density field, for example, simple liquids and colloidal suspensions. For a time-dependent change of external parameters, we show that the Jarzynski relation connecting work with the change of free energy holds if the time evolution of the density follows the Kawasaki-Dean equation. Specifically, we study the work distributions for the compression and expansion of a two-dimensional colloidal model suspension implementing a practical coarse-graining scheme of the microscopic particle positions. We demonstrate that even if coarse-grained dynamics and density functional do not match, the fluctuation relations for the work still hold albeit for a different, apparent, change of free energy.

Potential and flux field landscape theory. II. Non-equilibrium thermodynamics of spatially inhomogeneous stochastic dynamical systems

“…Third, spatially inhomogeneous systems have been largely unexplored in the context of stochastic thermodynamics, although there do exist a few studies in this context. 87,95 Since spatial inhomogeneity is typical of nonequilibrium systems, this issue is obviously important.…”

Finite element discretization of non-linear diffusion equations with thermal fluctuations

“…Note that the mobility depends on the position through its dependence on the concentration field and, therefore, such space integrals are not immediate. We will use the following ap- 4. In 2D, the Delaunay cell of node µ is surrounded by the triangular elements e. For each point of the triangular element e, there is a constant vector be→µ that points towards the node µ and that gives the derivative of the linear function ψµ(r) at that point.…”

“…Fluctuating equations of the form (2) have been considered in the DDFT literature 4 , where a debate on its physical meaning has arisen (see Ref.…”

“…Eq. (1) has become the focus of Dynamic Density Functional Theory (DDFT) for the study of dynamics of colloidal suspensions [1][2][3][4] . The two quantities that enter this equation are the free energy functional F [c] and the mobility coefficient Γ(c) that may depend, in general, on the concentration field.…”

Stochastic thermodynamics of hidden pumps

“…Some states are hidden and the resulting description of the system becomes "coarse grained." The thermodynamic implications of coarse graining is an active field of research [11][12][13][14][15][16][17][18][19][20][21]. The coarse-grained entropy production is typically lower than the actual one since it misses the positive contribution of the hidden edges.…”