While the origins of temporal correlations in Langevin dynamics have been thoroughly researched, the understanding of spatially correlated noise (SCN) is rather incomplete. In particular, very little is known about the relation between friction and SCN. In this article, starting from the microscopic, deterministic model, we derive the analytical formula for the spatial correlation function in the particle-bath interactions. This expression shows that SCN is the inherent component of binary mixtures, originating from the effective (entropic) interactions. Further, employing this spatial correlation function, we postulate the thermodynamically consistent Langevin equation driven by the Gaussian SCN and calculate the adequate fluctuation-dissipation relation. The thermodynamical consistency is achieved by introducing the spatially variant friction coefficient, which can be also derived analytically. This coefficient exhibits a number of intriguing properties, e.g., the singular behavior for certain types of interactions. Eventually, we apply this new theory to the system of two charged particles in the presence of counter-ions. Such particles interact via the screened-charge Yukawa potential and the inclusion of SCN leads to the emergence of the anomalous frictionless regime. In this regime the particles can experience active propulsion leading to the transient attraction effect. This effect suggests a nonequilibrium mechanism facilitating the molecular binding of the like-charged particles.

The problem of a spatially correlated noise affecting a complex system is studied in this paper. We present a comprehensive analysis of a two-dimensional model polymer chain, driven by the spatially correlated Gaussian noise, for which we have varied the amplitude and the correlation length. The chain model is based on a bead-spring approach, enriched with a global Lennard-Jones potential and angular interactions. We show that spatial correlations in the noise inhibit the chain geometry dynamics, enhancing the preservation of the polymer shape. This is supported by the analysis of correlation functions of both the module length and angles between neighboring modules, which have been measured for the noise amplitude ranging over three orders of magnitude. Moreover, we have observed the correlation length dependent bead motion synchronization and the spontaneous polymer unfolding, resulting from an interplay between chain potentials and the spatially structured noise.

While the density functional theory with integral equations techniques are very efficient tools in numerical analysis of complex fluids, an analytical insight into the phenomenon of effective interactions is still limited. In this paper we propose a theory of binary systems which results in a relatively simple analytical expression combining arbitrary microscopic potentials into the effective interaction. The derivation is based on translating many particle Hamiltonian including particle-depletant and depletant-depletant interactions into the occupation field language. Such transformation turns the partition function into multiple Gaussian integrals, regardless of what microscopic potentials are chosen. In result, we calculate the effective Hamiltonian and discuss when our formula is a dominant contribution to the effective interactions. Our theory allows us to analytically reproduce several important characteristics of systems under scrutiny. In particular, we analyze the effective attraction as a demixing factor in the binary systems of Gaussian particles, effective interactions in the binary mixtures of Yukawa particles and the system of particles consisting of both repulsive core and attractive/repulsive Yukawa interaction tail, for which we reproduce the 'attraction-through-repulsion' and 'repulsion-through-attraction' effects.