# When Do LLMs Reason? A Dynamical Systems View via Entropy Phase Transitions

arXiv: https://arxiv.org/abs/2605.22873 · HTML: https://mlsanity.com/paper/2605.22873/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 41 of its 44 references that are in the map.
- First posted on arXiv 20 May 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 41)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [ConceptNet 5.5: An Open Multilingual Graph of General Knowledge](https://mlsanity.com/paper/1612.03975/) (2016)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [Chain of Thought Empowers Transformers to Solve Inherently Serial Problems](https://mlsanity.com/paper/2402.12875/) (2024)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [Chain-of-Thought Reasoning Without Prompting](https://mlsanity.com/paper/2402.10200/) (2024)
- [MuSR: Testing the Limits of Chain-of-thought with Multistep Soft Reasoning](https://mlsanity.com/paper/2310.16049/) (2023)
- [Mind Your Step (by Step): Chain-of-Thought can Reduce Performance on Tasks where Thinking Makes Humans Worse](https://mlsanity.com/paper/2410.21333/) (2024)
- [BEST-Route: Adaptive LLM Routing with Test-Time Optimal Compute](https://mlsanity.com/paper/2506.22716/) (2025)
- [Think Only When You Need with Large Hybrid-Reasoning Models](https://mlsanity.com/paper/2505.14631/) (2025)
- [Rethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning](https://mlsanity.com/paper/2501.15602/) (2025)
- [Meta-Reasoner: Dynamic Guidance for Optimized Inference-time Reasoning in Large Language Models](https://mlsanity.com/paper/2502.19918/) (2025)
- [Reasoning Circuits in Language Models: A Mechanistic Interpretation of Syllogistic Inference](https://mlsanity.com/paper/2408.08590/) (2024)
- [Division-of-Thoughts: Harnessing Hybrid Language Model Synergy for Efficient On-Device Agents](https://mlsanity.com/paper/2502.04392/) (2025)
- [Think Just Enough: Sequence-Level Entropy as a Confidence Signal for LLM Reasoning](https://mlsanity.com/paper/2510.08146/) (2025)
- [Disentangling Logic: The Role of Context in Large Language Model Reasoning Capabilities](https://mlsanity.com/paper/2406.02787/) (2024)
- [Think Deep, Not Just Long: Measuring LLM Reasoning Effort via Deep-Thinking Tokens](https://mlsanity.com/paper/2602.13517/) (2026)
- [EvolveRouter: Co-Evolving Routing and Prompt for Multi-Agent Question Answering](https://mlsanity.com/paper/2604.05149/) (2026)
- [Route-and-Reason: Scaling Large Language Model Reasoning with Reinforced Model Router](https://mlsanity.com/paper/2506.05901/) (2025)

## Built on by (most cited first, 2 of 2)

- [Answer-Distribution Trajectories: A Stochastic-Dynamics View of LLM Reasoning](https://mlsanity.com/paper/2609.09030/) (2026)
- [Chain-of-Thought Entropy as a Reliability Signal: A Preregistered Reproduction](https://mlsanity.com/paper/2609.19606/) (2026)

## Abstract (arXiv)

Chain-of-thought (CoT) reasoning has become the default strategy for enhancing LLM capabilities, yet its application raises a fundamental question: when is explicit reasoning actually beneficial? Empirical evidence reveals a striking paradox: CoT often provides marginal or even negative gains on factual and open-ended tasks while multiplying token consumption. In this work, we show that LLM reasoning is not a static property of tasks or models, but a dynamic decoding state that emerges during generation. Through systematic analysis, we find early-stage entropy dynamics provide a reliable signal of this state: tasks benefiting from CoT exhibit consistent entropy reduction, while others display unstable or increasing patterns. This behavior can be interpreted as a phase-transition-like shift from a high-entropy exploratory regime to a low-entropy structured reasoning regime. Based on these insights, we propose EDRM (Entropy Dynamics-based Reasoning Manifold), a lightweight and training-free routing framework that leverages early decoding entropy to adaptively select inference strategies. EDRM embeds entropy trajectories into a compact and interpretable manifold representation, enabling both zero-shot deployment and fine-grained instance-level adaptation. Across 15 benchmarks and 4 LLMs of varying scales and architectures, EDRM consistently outperforms static baselines. At the dataset level, EDRM achieves 41--55% token reduction while improving accuracy with as few as 50 calibration samples. At the instance level, it further improves accuracy by up to 4.7% while maintaining 27--45% token savings. These results suggest that reasoning should be invoked selectively rather than by default, and demonstrate the effectiveness of entropy-driven decoding control for efficient and adaptive LLM inference.