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

Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis

We theoretically investigate an electric-field-driven system of charged spheres as a primitive model of concentrated electrolytes under an applied electric field. First, we provide a unified formulation for the stochastic charge and density dynamics of the electric-field-driven primitive model using the stochastic density functional theory (DFT). The stochastic DFT integrates the four frameworks (the equilibrium and dynamic DFTs, the liquid state theory and the field-theoretic approach), which allows us to justify in a unified manner various modifications previously made for the Poisson-Nernst-Planck model. Next, we consider stationary density-density and charge-charge correlation functions of the primitive model with a static electric field. We predict an electric-field-induced synchronization between emergences of density and charge oscillations. We are mainly concerned with the emergence of stripe states formed by segregation bands transverse to the external field, thereby demonstrating the following: (i) the electric-field-induced crossover occurs prior to the conventional Kirkwood crossover without an applied electric field, and (ii) the ion concentration dependence of the decay lengths at the onset of oscillations bears a similarity to the underscreening behavior found by recent simulation and theoretical studies on equilibrium electrolytes. Also, the 2D inverse Fourier transform of the correlation function illustrates the existence of stripe states beyond the electric-field-induced Kirkwood crossover.

A topological fluctuation theorem

Fluctuation theorems specify the non-zero probability to observe negative entropy production, contrary to a naive expectation from the second law of thermodynamics. For closed particle trajectories in a fluid, Stokes theorem can be used to give a geometric characterization of the entropy production. Building on this picture, we formulate a topological fluctuation theorem that depends only by the winding number around each vortex core and is insensitive to other aspects of the force. The probability is robust to local deformations of the particle trajectory, reminiscent of topologically protected modes in various classical and quantum systems. We demonstrate that entropy production is quantized in these strongly fluctuating systems, and it is controlled by a topological invariant. We demonstrate that the theorem holds even when the probability distributions are non-Gaussian functions of the generated heat.

Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling

The disordered and hyperuniform structures of densely packed spheres near and at jamming are characterized by vanishing of long-wavelength density fluctuations, or equivalently by long-range power-law decay of the direct correlation function (DCF). We focus on previous simulation results that exhibit the degradation of hyperuniformity in jammed structures while maintaining the long-range nature of the DCF to a certain length scale. Here we demonstrate that the field-theoretic formulation of stochastic density functional theory is relevant to explore the degradation mechanism. The strong-coupling expansion method of stochastic density functional theory is developed to obtain the metastable chemical potential considering the intermittent fluctuations in dense packings. The metastable chemical potential yields the analytical form of the metastable DCF that has a short-range cutoff inside the sphere while retaining the long-range power-law behavior. It is confirmed that the metastable DCF provides the zero-wavevector limit of the structure factor in quantitative agreement with the previous simulation results of degraded hyperuniformity. We can also predict the emergence of soft modes localized at the particle scale by plugging this metastable DCF into the linearized Dean-Kawasaki equation, a stochastic density functional equation.

Nonequilibrium Thermodynamics of Charge Separation in Organic Solar Cells

This work presents a novel theoretical description of the nonequilibrium thermodynamics of charge separation in organic solar cells (OSCs). Using stochastic thermodynamics, we take realistic state populations derived from the phonon-assisted dynamics of electron-hole pairs within photoexcited organic bilayers to connect the kinetics with the free energy profile of charge separation. Hereby, we quantify for the first time the difference between nonequilibrium and equilibrium free energy profile. We analyze the impact of energetic disorder and delocalization on free energy, average energy, and entropy. For a high disorder, the free energy profile is well-described as equilibrated. We observe significant deviations from equilibrium for delocalized electron-hole pairs at a small disorder, implying that charge separation in efficient OSCs proceeds via a cold but nonequilibrated pathway. Both a large Gibbs entropy and large initial electron-hole distance provide an efficient charge separation, while a decrease in the free energy barrier does not necessarily enhance charge separation.

Effective thermodynamics of two interacting underdamped Brownian particles

Starting from the stochastic thermodynamics description of two coupled underdamped Brownian particles, we showcase and compare three different coarse-graining schemes leading to an effective thermodynamic description for the first of the two particles: marginalization over one particle, bipartite structure with information flows, and the Hamiltonian of mean force formalism. In the limit of time-scale separation where the second particle with a fast relaxation time scale locally equilibrates with respect to the coordinates of the first slowly relaxing particle, the effective thermodynamics resulting from the first and third approach are shown to capture the full thermodynamics and to coincide with each other. In the bipartite approach, the slow part does not, in general, allow for an exact thermodynamic description as the entropic exchange between the particles is ignored. Physically, the second particle effectively becomes part of the heat reservoir. In the limit where the second particle becomes heavy and thus deterministic, the effective thermodynamics of the first two coarse-graining methods coincide with the full one. The Hamiltonian of mean force formalism, however, is shown to be incompatible with that limit. Physically, the second particle becomes a work source. These theoretical results are illustrated using an exactly solvable harmonic model.

Stochastic thermodynamics of hidden pumps

We show that a reversible pumping mechanism operating between two states of a kinetic network can give rise to Poisson transitions between these two states. An external observer, for whom the pumping mechanism is not accessible, will observe a Markov chain satisfying local detailed balance with an emerging effective force induced by the hidden pump. Due to the reversibility of the pump, the actual entropy production turns out to be lower than the coarse-grained entropy production estimated from the flows and affinities of the resulting Markov chain. Moreover, in presence of a large time scale separation between the fast-pumping dynamics and the slow-network dynamics, a finite current with zero dissipation may be produced. We make use of these general results to build a synthetase-like kinetic scheme able to reversibly produce high free-energy molecules at a finite rate and a rotatory motor achieving 100% efficiency at finite speed.