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Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, the familiar linear operator techniques that one would then hope to use often fail… (More)

- Paul M. Riechers
- 2018

Framing computation as the transformation of metastable memories, we explore its fundamental thermodynamic limits. The true power of information follows from a novel decomposition of nonequilibrium… (More)

Santa Fe Institute Working Paper 15-10-041 arxiv.org:1510.08186 [physics.quant-ph] Minimized State-Complexity of Quantum-Encoded Cryptic Processes Paul M. Riechers, ∗ John R. Mahoney, † Cina… (More)

- Paul M. Riechers, Dowman P. Varn, James P. Crutchfield
- Acta crystallographica. Section A, Foundations…
- 2014

Given a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, analytical expressions are developed for the pairwise correlation functions… (More)

Maintained by environmental fluxes, biological systems are thermodynamic processes that operate far from equilibrium without detailed-balanced dynamics. Yet, they often exhibit well defined… (More)

- Alexander B. Boyd, Dibyendu Mandal, Paul M. Riechers, James P. Crutchfield
- Physical review letters
- 2017

A central result that arose in applying information theory to the stochastic thermodynamics of nonlinear dynamical systems is the information-processing second law (IPSL): the physical entropy of the… (More)

Abstract We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to… (More)

- Paul M. Riechers, Dowman P. Varn, James P. Crutchfield
- ArXiv
- 2014

We recently derived analytical expressions for the pairwise (auto)correlation
functions (CFs) between modular layers (MLs) in close-packed structures (CPSs) for the wide
class of stacking processes… (More)

- Paul M. Riechers, James P. Crutchfield
- Chaos
- 2018

The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the… (More)

Spectral Simplicity of Apparent Complexity, Part I: The Nondiagonalizable Metadynamics of Prediction

- Paul M. Riechers, James P. Crutchfield
- Chaos
- 2017

Virtually all questions that one can ask about the behavioral and structural complexity of a stochastic process reduce to a linear algebraic framing of a time evolution governed by an appropriate… (More)