Infomechanics: Unifying Physics, Thermodynamics & Inference

• Infomechanics is an interdisciplinary framework that treats information as a quantifiable state variable, unifying thermodynamics, statistical mechanics, and computation.
• It employs Bayesian updating, conservation laws, and entropy equivalence to derive physical laws and efficient inference procedures.
• The framework extends to non-equilibrium, quantum, and computational systems, offering innovative insights for experiment design and learning algorithms.

Information Mechanics (Infomechanics) is an interdisciplinary framework that unifies thermodynamics, statistical mechanics, information theory, and computational inference by recasting the laws of physics, learning, and computation as consequences of information-theoretic principles. In Infomechanics, information is treated as a state variable, akin to entropy and energy, with quantifiable mathematical relations and conservation laws that govern both physical processes and formal inference procedures. This approach encompasses both equilibrium and non-equilibrium phenomena, classical and quantum regimes, and even the design of experiments and learning algorithms.

1. Foundations and Mathematical Principles

Infomechanics extends the Jaynesian view of statistical mechanics—"probability as logic"—to all levels of physical and computational systems. The core tenet is that the observable properties, dynamics, and laws governing a system derive from the observer’s available information and its quantification through consistent valuation.

• Valuations on Ordered Structures: Any partially ordered set (poset) can be quantified using real-valued valuations and bivaluations, leading to sum and product rules for probabilities and entropies. This underlies probability theory, quantum amplitudes (via sum–product rules), and even the Minkowski metric in relativity (Knuth, 2010).
• Information as a Quantifiable State Variable: Information is not simply negative entropy. Given a system with Θ distinguishable categories and success probability p for a task, the information is defined as $I = k\,\log(\Theta\,p)$, with $k$ a constant (Lin et al., 2016). More generally, when data is subject to constraints (such as mean energy in statistical mechanics), the maximum-entropy principle yields the Gibbs distribution as the least-biased inference.
• Shannon and Gibbs Entropy Equivalence: The quantitative equivalence between statistical mechanical entropy ($S_{\rm Gibbs}=-k_B\sum_i p_i\ln p_i$) and Shannon entropy ($H_{\rm Shannon} = -\sum_i p_i\log_2 p_i$) is exact, $S = k_B\ln(2)H_{\rm Shannon}$, demonstrating that disorder in condensed matter is fundamentally informational (Fisher et al., 1 Dec 2025).
• Conservation Laws in Bayesian Inference: For any latent variable $x$ and data $D$, the pointwise conservation $S(x)+i(x)=S_0(x)$ (where $S$ is posterior surprisal, $S_0$ prior, $i$ information gain) gives two additive projections: conservation of Shannon entropy and Fisher information, leading to unique state functionals invariant under coordinate transformations (Isomura, 21 Jan 2026).

2. Thermodynamics, Statistical Mechanics, and Information Theory

Infomechanics provides a fully unified account of entropy, free energy, and irreversibility:

• Statistical Ensembles as States of Knowledge: The canonical, microcanonical, and grand-canonical ensembles emerge by adding or removing information constraints on averages, with all mechanical relations (partition functions, free energies, etc.) generated via Bayesian updating and maximum-entropy principles (Rogers et al., 2011, Spalvieri, 2022, Chakraborty, 2024).
• Work Extraction and the Mechanics of Information: The capacity of a thermodynamic system to perform work is directly tied to information content—it is only non-equilibrium information that can be expended for work, not the “locked” equilibrium information (Lin et al., 2016). The explicit work–information relation for gas expansion is $W=E\,[1 - \exp(-2I/(3N))]$.
• Thermodynamics of Information-Processing: Information acts as a thermodynamic resource, modifying the second law. Erasing one bit requires at least $k_B T\ln2$ of dissipated energy (Landauer's principle). Mutual information between measurement and system bounds the maximum extractable work in measurement-feedback cycles (e.g., the Szilard engine), with the extended second law $W_{\text{fb}}\geq\Delta F - T I(X;M)$ (Parrondo, 2023).
• Information Carnot Machines: Information transmission and amplification, for example by binary pulse trains in optical fibers, is thermodynamically equivalent to a Carnot cycle, establishing that the entropy per bit is a literal thermodynamic state variable ($k_B\ln2$) and linking communication efficiency to Carnot efficiency (0705.2535).

3. Non-Equilibrium, Kinetics, and Information Dynamics

Infomechanics generalizes to non-equilibrium systems and time-dependent processes:

• Kinetic Theory of Information: In Hamiltonian many-body systems, the $N$-particle information density $\mathcal{I}_N$ is strictly conserved in phase space (Liouville’s theorem). Reducing to the 1-particle information density via an information-BBGKY hierarchy yields a Boltzmann-type equation for entropy production with the Kolmogorov entropy rate as the information generation term (Treumann et al., 2015).
• Non-Equilibrium Free Energy and Entropy Production: The process-level free energy for path ensembles, subject to path-wise flux constraints, yields fluctuation–dissipation theorems valid far from equilibrium. Entropy production equals the Kullback–Leibler divergence between forward and reverse process path probabilities (Rogers et al., 2011).
• Information Geometry and Computational Complexity: The only robust, coordinate-invariant state functions are Shannon entropy and the trace of Fisher information. Their non-additive combination, the information potential $\Phi[p]=H[p] + \frac{N}{2}\log(J[p]/(2\pi e N))$, quantifies the “ruggedness” of the inference landscape and scales as the log-number of local minima at low temperature, establishing an information–computation exchange principle (Isomura, 21 Jan 2026).

4. Infomechanics in Quantum Theory and Stochastic Mechanics

Information-theoretic principles underpin both classical and quantum stochastic dynamics:

• Stochastic Variational Principles with Information Constraints: The action for stochastic paths is augmented by relative entropy (Kullback–Leibler) and Fisher information terms, imposing indistinguishability of forward/backward path densities and penalizing sharpness. Variation yields coupled stochastic Euler–Lagrange equations whose solution reproduces the full Schrödinger equation and Born rule (Yang, 2021).
• Quantum Measurement and Decoherence: Information as “copyability” (the ability to be cloned across systems or observers) identifies the classical world as that in which quantum superposition branches have been irreversibly and redundantly copied into the environment, rendering them effectively distinguishable. The preferred basis arises from interaction locality, and irreversible “collapse” follows from environmental propagation of copies (Ostrowski, 2010).
• Quantum Mechanics from Information Loss at Horizons: Quantum randomness and the path-integral formalism emerge directly from maximizing entropy under causal constraints (e.g., Rindler horizons), implying quantum mechanics is not fundamental but a consequence of information theory plus relativistic causal structure (Lee, 2010).

5. Computational and Structural Information Mechanics

Infomechanics quantifies not only physical and stochastic systems but the structure of computation and learning:

• Structural Complexity and Channel Analysis: Computational mechanics models structured transformations (channels) between input and output processes via the unique, minimal ε-transducer, whose causal states exactly capture the information flow, memory, and complexity (statistical complexity, excess entropy, crypticity) of channels (Barnett et al., 2014).
• Information-Theoretic Learning and Inference: Model-free machine learning becomes “learning as measuring” uncertainty: each datum’s surprisal, defined as $I(x) = -\log p(x)$, is the primitive quantity. Inference (prediction, generative, anomaly detection, causality, time series) relies only on measuring and reweighting surprisals and their derivatives (e.g., via Laplacian distances), not fitting latent global models. This provides full interpretability, immediate updates under data edits, and direct measurement of information transfer and generalization (Hazard et al., 26 Oct 2025).
• Optimization of Experiment Design: Stress-state entropy quantifies the information content of mechanical test specimens. Specimen optimization via entropy maximization (or minimization for specific goals) enables identification of rich, efficient mechanical tests, balancing informativeness and noise-robustness, and enabling transfer of parameters between different experimental protocols of equal entropy (Ihuaenyi et al., 14 Jan 2025).

6. Extensions: Classical Measurement, Bayesian Epistemology, and Information Conservation

• Measurement-Induced Disturbance in Classical Mechanics: Even classical Hamiltonian systems, when measured by finite-precision devices, exhibit a precision–disturbance trade-off analogous to the quantum uncertainty relation, with a fundamental apparatus-dependent constant $q̄$. Bayesian epistemology of classical measurements thus exposes non-trivial information constraints and entropy production, paralleling decoherence and collapse (Theurel, 2021).
• Conditional Entropy and Ensemble Equivalence: The conditional equiprobability of microstates given macrostates shows that the famous Boltzmann–Planck entropy is the conditional entropy of microstates given a fixed macrostate. All statistical ensembles become simple statements about which features are held fixed or treated as random variables, and all quantum corrections emerge from retaining exact combinatorial structure (Spalvieri, 2022).
• Compression-Based Measurement of Physical Entropies: Operationally, the bit-length of minimally compressed data (over atomic-scale configurations) recovers the thermodynamic entropy directly, without partitioning or empirical models, establishing information as the fundamental measure of physical disorder (Fisher et al., 1 Dec 2025).

7. Outlook and Significance

Infomechanics provides an algorithm-independent, unified foundation for understanding the mechanics of uncertainty, irreversibility, learning, and computation across physical, biological, and artificial systems. All laws—thermodynamic, quantum, dynamical, and inferential—arise as necessary consequences of information quantification and conservation, tightly linking entropy, information gain, and computational complexity. Open directions include further development of information-computation exchange laws, generalizations to quantum gravity and causal sets, information-based experiment design, and the role of information in complexity and emergence (Isomura, 21 Jan 2026, Knuth, 2010).

Key references: (Rogers et al., 2011, Lin et al., 2016, Parrondo, 2023, Spalvieri, 2022, Treumann et al., 2015, Yang, 2021, Barnett et al., 2014, Ihuaenyi et al., 14 Jan 2025, Fisher et al., 1 Dec 2025, Hazard et al., 26 Oct 2025, Isomura, 21 Jan 2026, Chakraborty, 2024, Theurel, 2021, Lee, 2010, 0705.2535, Knuth, 2010, Ostrowski, 2010).