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TEG: Exascale Cluster Governance via Non-Equilibrium Thermodynamics and Langevin Dynamics

Zhengyan Chu

TL;DR

TEG (Thermo-Economic Governor), a decentralized architecture that establishes a rigorous topological isomorphism between cluster resource contention and many-body physics, demonstrates that emergent order, rather than deterministic control, is the necessary condition for Exascale scalability.

Abstract

As cloud computing scales toward the Exascale regime ($10^5+$ nodes), the prevailing "Newtonian" orchestration paradigm -- exemplified by Kubernetes -- approaches fundamental physical limits. The centralized, deterministic scheduling model suffers from $O(N)$ latency scaling, "Head-of-Line" blocking, and thermodynamic blindness, rendering it incapable of managing the stochastic chaos of next-generation AI workloads. This paper proposes a paradigm shift from orchestration to Thermodynamic Governance. We model the compute cluster not as a static state machine, but as a Dissipative Structure far from equilibrium. We introduce TEG (Thermo-Economic Governor), a decentralized architecture that establishes a rigorous topological isomorphism between cluster resource contention and many-body physics. TEG replaces the global scheduler with Langevin Agents that execute Brownian motion on a Holographic Potential Field, reducing decision complexity to $O(1)$. System stability is maintained via a macro-scale Landau Phase Transition mechanism, which modulates global damping (taxation) to physically dissolve deadlocks. Crucially, we enforce Token Evaporation to mirror entropy dissipation, preventing economic inflation and ensuring an open thermodynamic system. We provide formal theoretical analysis proving that: (1) The system converges asymptotically to a Nash Equilibrium via Dual-Number Damping; (2) OOM catastrophic failures are converted into manageable Glassy States via an OS-level Airlock Mutex; and (3) Safety is mathematically guaranteed under high inertia using High-Order Control Barrier Functions (HOCBF). TEG demonstrates that emergent order, rather than deterministic control, is the necessary condition for Exascale scalability.

TEG: Exascale Cluster Governance via Non-Equilibrium Thermodynamics and Langevin Dynamics

TL;DR

TEG (Thermo-Economic Governor), a decentralized architecture that establishes a rigorous topological isomorphism between cluster resource contention and many-body physics, demonstrates that emergent order, rather than deterministic control, is the necessary condition for Exascale scalability.

Abstract

As cloud computing scales toward the Exascale regime ( nodes), the prevailing "Newtonian" orchestration paradigm -- exemplified by Kubernetes -- approaches fundamental physical limits. The centralized, deterministic scheduling model suffers from latency scaling, "Head-of-Line" blocking, and thermodynamic blindness, rendering it incapable of managing the stochastic chaos of next-generation AI workloads. This paper proposes a paradigm shift from orchestration to Thermodynamic Governance. We model the compute cluster not as a static state machine, but as a Dissipative Structure far from equilibrium. We introduce TEG (Thermo-Economic Governor), a decentralized architecture that establishes a rigorous topological isomorphism between cluster resource contention and many-body physics. TEG replaces the global scheduler with Langevin Agents that execute Brownian motion on a Holographic Potential Field, reducing decision complexity to . System stability is maintained via a macro-scale Landau Phase Transition mechanism, which modulates global damping (taxation) to physically dissolve deadlocks. Crucially, we enforce Token Evaporation to mirror entropy dissipation, preventing economic inflation and ensuring an open thermodynamic system. We provide formal theoretical analysis proving that: (1) The system converges asymptotically to a Nash Equilibrium via Dual-Number Damping; (2) OOM catastrophic failures are converted into manageable Glassy States via an OS-level Airlock Mutex; and (3) Safety is mathematically guaranteed under high inertia using High-Order Control Barrier Functions (HOCBF). TEG demonstrates that emergent order, rather than deterministic control, is the necessary condition for Exascale scalability.
Paper Structure (42 sections, 3 theorems, 26 equations)

This paper contains 42 sections, 3 theorems, 26 equations.

Table of Contents

  1. Introduction
  2. The Exascale Scalability and Sustainability Challenge
  3. The Exascale Dilemma: Hitting the Physical Wall
  4. The Mismatch of Deterministic Orchestration
  5. Our Approach: Physics-Informed Thermo-Economic Scheduling
  6. Background and Related Work
  7. Centralized Cluster Orchestration
  8. Market-Based Resource Allocation
  9. Theoretical Foundation: Thermodynamics in Computing
  10. The Latency Collapse: A Queueing Theoretic View
  11. Resource Rigidities: The Fear Premium
  12. Thermal Efficiency: Exploiting COP Nonlinearity
  13. System Design
  14. Architecture Overview
  15. The Holographic Thermo-Economic Field
  16. ...and 27 more sections

Key Result

theorem 1

The control force field $\mathbf{F}_{ctrl}$ on the Riemannian manifold $\Omega$ can be uniquely decomposed into two orthogonal subspaces: the Gradient Subspace (Optimization) and the Curl Subspace (Sorting). Any manipulation of the vector potential $\mathbf{A}$ (to alter sorting logic) implies zero projection onto the scalar potential $\Phi$, ensuring that the "definition of optimality" remains i

Theorems & Definitions (6)

  • theorem 1: Orthogonal Control Subspaces
  • proof
  • theorem 2: Asymptotic Stability via Dual-Number Damping
  • proof
  • theorem 3: Inertia-Compensated Safety
  • proof