Communication-Induced Bifurcation and Collective Dynamics in Power Packet Networks: A Thermodynamic Approach to Information-Constrained Energy Grids

Abstract

This paper investigates the nonlinear dynamics and phase transitions in power packet network connected with routers, conceptualized as macroscopic information-ratchets. In the emerging paradigm of cyber-physical energy systems, the interplay between stochastic energy fluctuations and the thermodynamic cost of control information defines fundamental operational limits. We first formulate the dynamics of a single router using a Langevin framework, incorporating an exponential cost function for information acquisition. Our analysis reveals a discontinuous (first-order) phase transition, where the system adopts a strategic abandon of regulation as noise intensity exceeds a critical threshold $D_c$. This transition represents a fundamental information-barrier inherent to autonomous energy management. Here, we extend this model to network configurations, where multiple routers are linked through diffusive coupling, sharing energy between them. We demonstrate that the network topology and coupling strength significantly extend the bifurcation points, with collective resilient behaviors against local fluctuations. These results provide a rigorous mathematical basis for the design of future complex communication-energy network, suggesting that the stability of proposed systems is governed by the synergistic balance between physical energy flow and the thermodynamics of information exchange. It will serve to design future complex communication-energy networks, including internal energy management for autonomous robots.

Figures (6)

• Figure 1: Concept of power packet and its physical modeling as an information-ratchet. (a) Structure of a power packet, where the information payload (header and footer) is physically integrated and transmitted simultaneously with the energy unit. (b) Schematic of a power packet router, which operates as a Maxwell’s demon by processing the integrated information to regulate stochastic energy flows. (c) Equivalent dynamical model under information-constrained feedback. The control input $u$ is determined by the information co-transmitted with the packet, incurring a thermodynamic cost $\Phi(u)$ that acts as a nonlinear feedback to the Langevin dynamics.
• Figure 2: Thermodynamic trade-off between energy and information. Profile of the system evaluation function $J$ (thick blue line) against control amount $u$. While the gain for satisfying demand response (dotted green line) saturates, the information processing cost (dotted red line) increases exponentially. It is shown that the global optimal solution $u^*$ (dotted yellow line) is obtained in a region where energy and entropy are balanced.
• Figure 3: Autonomous adaptation of control to environmental noise. Showing the change in evaluation function $J$ with increasing environmental noise intensity $D(t)$. As noise becomes more severe, dissipation costs associated with information processing become dominant, and the system autonomously shifts $u^*$ to the low-output side to avoid excessive energy consumption.
• Figure 4: Bifurcation diagram of discontinuous phase transition. Showing a discontinuous (first-order) phase transition where $u^*$ drops vertically to 0 the moment noise $D(t)$ exceeds the critical value $D_c$. At the critical value $D_c \approx 2.21$, the system shifts discontinuously from an ordered phase to a disordered phase. This corresponds to a state where the system autonomously abandons control to provide thermodynamic suppression because the dissipation cost of information has overwhelmed the gain of order formation.
• Figure 5: Dynamic optimization and loss decomposition under pseudo-solar supply by adaptive control strategy under communication constraints. (Top) Fluctuations in pseudo-solar output and the resulting transition of environmental entropy influx intensity. (Middle) Real-time transition of optimal control effort $u^*$ (adaptive ratchet) according to estimated noise intensity. (Bottom) Stacked chart showing the dynamic balance between energy dissipation due to information processing (red) and quality loss due to residual entropy (purple).