arXiv subjects

Nathaniel Rupprecht

Publications and source records attributed to Nathaniel Rupprecht.

6 recordsLinked to original sources

arXiv2020

Predictive Maxwell's Demons

Here we study the operation efficiency of a finite-size finite-response-time Maxwell's demon, who can make future predictions. We compare the heat and mass transport rate of predictive demons to non-predictive ones and find that predictive demons can achieve higher mass and heat transport rates over longer periods of time. We determine how the demon performance varies with response time, future sight, and the density of the gasses on which they operate.

cond-mat.stat-mech↗

arXiv2020

Depletion force between disordered linear macromolecules

When two macromolecules come very near in a fluid, the surrounding molecules, having finite volume, are less likely to get in between. This leads to a pressure difference manifesting as an entropic attraction, called depletion force. Here we calculate the density profile of liquid molecules surrounding a disordered rigid macromolecules modelled as a random arrangement of hard spheres on a linear backbone. We analytically determine the position dependence of the depletion force between two such disordered molecules by calculating the free energy of the system. We then use molecular dynamics simulations to obtain the depletion force between stiff disordered polymers as well as flexible ones and compare the two against each other. We also show how the disorder averaging can be handled starting from the inhomogenous RISM equations.

cond-mat.soft↗

arXiv2019

Maxwell's demons with finite size and response time

Nearly all theoretical analyses of the Maxwell's demon focus on its energetic and entropic costs of operation. Here, we focus on its rate of operation. In our model, a demon's rate limitation stems from its finite response time and gate area. We determine the rate limits of mass and energy transfer, as well as entropic reduction for four such demons: Those that select particles according to (1) direction, (2) energy, (3) number and (4) entropy. Lastly, we determine the optimal gate size for a demon with small, finite response time, and compare our predictions with molecular dynamics simulations with both ideal and non-ideal gasses. Lastly, we study the conditions under which the demons are able to move both energy and particles in the chosen direction when attempting to only move one.

cond-mat.stat-mech↗

arXiv2019

Enhancing the predictability and retrodictability of stochastic processes

Scientific inference involves obtaining the unknown properties or behavior of a system in the light of what is known, typically, without changing the system. Here we propose an alternative to this approach: a system can be modified in a targeted way, preferably by a small amount, so that its properties and behavior can be inferred more successfully. For the sake of concreteness we focus on inferring the future and past of Markov processes and illustrate our method on two classes of processes: diffusion on random spatial networks, and thermalizing quantum systems.

cond-mat.stat-mech↗

arXiv2018

Limits on Inferring the Past

Here we define and study the properties of retrodictive inference. We derive equations relating retrodiction entropy and thermodynamic entropy, and as a special case, show that under equilibrium conditions, the two are identical. We demonstrate relations involving the KL-divergence and retrodiction probability, and bound the time rate of change of retrodiction entropy. As a specific case, we invert various Langevin processes, inferring the initial condition of \(N\) particles given their final positions at some later time. We evaluate the retrodiction entropy for Langevin dynamics exactly for special cases, and find that one's ability to infer the initial state of a system can exhibit two possible qualitative behaviors depending on the potential energy landscape, either decreasing indefinitely, or asymptotically approaching a fixed value. We also study how well we can retrodict points that evolve based on the logistic map. We find singular changes in the retrodictivity near bifurcations. Counterintuitively, the transition to chaos is accompanied by maximal retrodictability.

stat.OT↗

arXiv2017

Collective Motion of Predictive Swarms

Theoretical models of populations and swarms typically start with the assumption that the motion of agents is governed by the local stimuli. However, an intelligent agent, with some understanding of the laws that govern its habitat, can anticipate the future, and make predictions to gather resources more efficiently. Here we study a specific model of this kind, where agents aim to maximize their consumption of a diffusing resource, by attempting to predict the future of a resource field and the actions of other agents. Once the agents make a prediction, they are attracted to move towards regions that have, and will have, denser resources. We find that the further the agents attempt to see into the future, the more their attempts at prediction fail, and the less resources they consume. We also study the case where predictive agents compete against non-predictive agents and find the predictors perform better than the non-predictors only when their relative numbers are very small. We conclude that predictivity pays off either when the predictors do not see too far into the future or the number of predictors is small.

nlin.AO↗