# Path Integral Solution for Dissipative Generative Dynamics

arXiv: https://arxiv.org/abs/2601.00860 · HTML: https://mlsanity.com/paper/2601.00860/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 30 Dec 2025.

## Builds on (most cited first, 6 of 6)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)

## Abstract (arXiv)

Can purely mechanical systems generate intelligent language? We prove that dissipative quantum dynamics with analytically tractable non-local context aggregation produce coherent text generation, while conservation laws cause fundamental failure. Employing Koopman operators with closed-form path integral propagators, we show irreversible computation fundamentally requires both controlled information dissipation and causal context aggregation. Spectral analysis reveals emergent eigenvalue structure, separating into decay modes (forgetting), growth modes (amplification), and neutral modes (preservation) -- the essential ingredients for directed information flow. Hamiltonian constraints force the elimination of these dissipative modes and degrading performance despite unchanged model capacity. This establishes language generation as dissipative quantum field theory, proving mechanical systems acquire intelligence through the combination of dissipation and non-locality, not through conservation.