Memory-controlled random bit generator

TL;DR

The paper investigates how binary information can be stored and manipulated in a microscopic system by exploiting memory effects in a viscoelastic bath. It models a Brownian particle in a spatially periodic potential under periodic driving, governed by a Generalized Langevin Equation with memory kernel, where the memory time $\tau$ determines whether the period-averaged velocity serves as a bistable bit or a chaotic random-bit generator. A memory-switching protocol toggles $\tau$ between $0.1$ and $0.01$ every $N$ driving periods to generate a bit stream, with randomness quantified by the normalized Shannon entropy $H(n,N)/H_{rand}(n)$ approaching 1 for $N\ge 5$ and $n\le 8$, and a Kramers-like analysis yields an energy barrier $\Delta E \approx 0.0177$ to ensure stability. An effective-mass correspondence $m^* = m - \Delta m$ with $\Delta m = \gamma \int_0^\infty t K(t) dt$ links memoryful and memoryless descriptions, underscoring the generality of memory-based information processing in microscale viscoelastic environments.

Abstract

Nowadays a bit is no longer a mere abstraction but a physical quantity whose manipulation governs both operation of modern technologies and theoretical frontiers of fundamental science. In this work we propose a setup in which the memory time can be utilized to control the generation and storage of binary information. In particular, we consider a nonequilibrium Brownian particle immersed in a viscoelastic environment and dwelling in a spatially periodic potential. We interpret its average velocity as a bit and show that depending on the memory time characterizing the viscoelastic bath the particle can be either in one of two stable states representing the bit values or in a chaotic state in which the information is erased and a new bit can be generated. We analyze randomness of the so obtained bit sequence and assess the stability of the produced values. Our study provides a blueprint for storing and processing information in a microscopic system using its memory.

Figures (5)

• Figure 1: (a) "Bifurcation" diagram of the period-averaged velocity $\mathsf{v}(t)$ as a function of the memory time $\tau$. In (b) and (c) exemplary trajectories for $\tau=0.01$ and $\tau = 0.1$ are pictured.
• Figure 2: (a) "Bifurcation" diagram of the period-averaged velocity $\mathsf{v}$ for the approximate system in the effective mass approach as a function of the mass correction $\Delta m = \tau$. (b) Corresponding maximal Lyapunov exponent $\lambda_\mathrm{max}$ in the deterministic limit $\theta=0$ estimated using the method of reconstruction of the attractor based on the particle's trajectory Rosenstein1993.
• Figure 3: Time evolution of the period-averaged velocity $\mathsf{v}(t)$. The memory time $\tau$ switches between values $0.01$ and $0.1$ every $N = 100$ periods of the driving force $\mathsf{T}$. The corresponding bit sequence is "$10110100$".
• Figure 4: Normalized Shannon entropy $H(n, N)/H_\mathrm{rand}(n)$ of the bit segments of length $n$ as a function of the number of chaotic periods $N$.
• Figure 5: Logarithm of the mean escape time $\tau_\mathrm{e}$ from the attractors corresponding to the bistable period-averaged velocity states as a function of the inverse temperature $1/\theta$. The straight line is fitted to simulation results for the intermediate temperatures $\theta \in [0.002, 0.01]$.