Reintroducing Intergenerational Equilibrium: Key Concepts behind the New Polish Pension System

Poland adopted a new pension system in 1999. This new pension system allows Poland to reduce pension expenditure (as a percent of GDP), instead of increasing it – as is projected for the majority of other OECD countries. This paper presents the conceptual background of the new system design. The new system’s long-term objective is to ensure intergenerational equilibrium irrespective of the demographic situation. This requires stabilisation of the share of GDP allocated to the entire retired generation. Traditional pension systems aim, instead, at stabilisation of the share of GDP per retiree. The change in demographic structure observed over the past for a couple of decades and this historic attempt to stabilise the share of GDP per retiree led to severe fiscal problems and negative externalities for growth, as observed in numerous countries. Many countries have tried to reform their pension systems in different ways to try to resolve the issue of these ever-increasing costs. Although the Polish reform uses a number of techniques applied elsewhere, its design differs from the typical approaches – and the lessons and results are promising for all OECD countries. This paper presents the theoretical and practical application of this alternative approach and as such, the key features of the new Polish pension system design.pensions, equilibrium, GDP, pension debt servicing, income allocation, generations

Thermodynamically consistent Langevin dynamics with spatially correlated noise predicts frictionless regime and transient attraction effect

While the origin 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, we derive the formal 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 SCN and 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 interaction types. 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 non-equilibrium mechanism facilitating the molecular binding of the like-charged particles.Comment: expanded and revised version resubmitted to Phys. Rev.

Non-Gaussian polymers described by alpha-stable chain statistics: model, applications and effective interactions in binary mixtures

The Gaussian chain model is the classical description of a polymeric chain, which provides the analytical results regarding end-to-end distance, the distribution of segments around the mass center of a chain, coarse grained interactions between two chains and effective interactions in binary mixtures. This hierarchy of results can be calculated thanks to the alpha stability of the Gaussian distribution. In this paper we show that it is possible to generalize the model of Gaussian chain to the entire class of alpha stable distributions, obtaining the analogous hierarchy of results expressed by the analytical closed-form formulas in the Fourier space. This allows us to establish the alpha-stable chain model. We begin with reviewing the applications of Levy flights in the context of polymer sciences, which include: chains with heavy-tailed distributions of persistence length, polymers adsorbed to the surface and the chains driven by a noise with power-law spatial correlations. Further, we derive the distribution of segments around the mass center of the alpha-stable chain and the coarse-grained interaction potential between two chains is constructed. These results are employed to discuss the model of binary mixture consisting of the alpha-stable chains. On what follows, we establish the spinodal decomposition condition generalized to the particles described by the shape of alpha-stable distributions. This condition is finally applied to analyze the on-surface phase separation of adsorbed polymers, which are known to be described with heavy tailed statistics.Comment: Complete version prepared for submission to Phys. Rev.

Selections and their Absolutely Continuous Invariant Measures

Let $I=[0,1]$ and consider disjoint closed regions $G_{1},....,G_{n}$ in $I\times I$ and subintervals $I_{1},......,I_{n},$ such that $G_{i}$ projects onto $I_{i.}$ We define the lower and upper maps $\tau_{1},$ $\tau_{2}$ by the lower and upper boundaries of $G_{i},i=1,....,n,$ respectively. We assume $\tau_{1}$, $\tau_{2}$ to be piecewise monotonic and preserving continuous invariant measures $\mu_{1}$ and $\mu_{2}$, respectively. Let $$ and $F^{(2)}$ be the distribution functions of $\mu_{1}$ and $\mu_{2}.$ The main results shows that for any convex combination $F$ of $$ and $F^{(2)}$ we can find a map $\eta$ with values between the graphs of $\tau_{1}$ and $\tau_{2}$ (that is, a selection) such that $F$ is the $\eta$-invariant distribution function. Examples are presented. We also study the relationship of the dynamics of multi-valued maps to random maps