Information Transduction, Variational Free Energy and Finite-Time Landauer Bounds: From Latent EEG Trajectories to a Thermodynamically Grounded Energy–GCI Limit

A thermodynamically and statistically grounded version of the Information Transductionand Dissonance Reduction (ITDR) framework is presented, in which “dissonance energy” isidentified with the variational free energy (VFE, in nats) of an explicitly specified hierarchical Gaussian generative model for EEG. To connect VFE to lower bounds on dissipationQ, the analysis employs (i) an explicit calculation of the squared Wasserstein distance W 22between recognition distributions qpre and qpost in latent space, (ii) finite-time Landauerprinciples for overdamped Langevin dynamics and their geometric generalizations that relate Q to W22 /τ (Proesmans et al., 2020; Scandi et al., 2022; Oikawa et al., 2025; Vu andSaito, 2021). The latent space ψ is interpreted as a set of phase–amplitude coordinates ofa small number of cortical oscillators, for which an overdamped Langevin approximationis formulated and the conditions under which W2(qpre, qpost) provides a lower bound onphysical dissipation without hidden scale factors are made explicit. A sharp distinction isdrawn between (a) information-processing energy κ∆E (nats→J) and (b) Landauer heatQ for irreversible erasure ∆S (bits→J); these quantities are not conflated in formulatingthe Energy–GCI limit. For n = 20 participants, 64-channel EEG is analysed during visualstimulation at 144 Hz with a fractal “benchmark” stimulus versus a phase-scrambled control. Two separate preprocessing pipelines are applied (1–100 Hz and narrowband around144 Hz), together with source reconstruction, artifact control (photodiode–EEG coherence,empty-room spectra, spatial filtering), mixed-effects models with cluster-robust errors, andpermutation checks. It is shown that (i) Target > Control in ciPLV/dwPLI, beta power andglobal coherence index (GCI); (ii) out-of-sample log predictive density and cross-validatedVFE confirm genuine reductions in prediction error; (iii) the rate of VFE reduction −d∆E/dtis positively associated with beta bursts in mixed-effects models that account for autocorrelation and covariates. A distribution-only dissipation estimator, validated in (Oikawa et al.,2025), is applied to q(ψt) trajectories, yielding calibrated intervals for Q(τ ) without potential reconstruction. The roles of strong coupling and quantum corrections (Vu and Saito,2021) (negligible at neural time scales) are clarified, and connections are drawn to Paretosubsystem decompositions of thermodynamic costs (Vu and Saito, 2024) and variational formulations that optimise terminal distributions under task constraints (VarOT, 2025). Theresulting Energy–GCI bound is explicitly falsifiable and can be directly linked to futurecalorimetric and haemodynamic measurements.