Mechanical plasticity as a unifying axis for the thermodynamics of biological information machines

<title>Abstract</title> <p> Biological machines that process information—ribosomes, ion pumps, synapses, and chromatin—span more than ten orders of magnitude in operating timescale and are usually analyzed one class at a time, with disjoint formalisms for translation fidelity, transport work, and synaptic memory. We introduce a single mechanical parameter, <italic>γ</italic> = <italic>k</italic> _{<italic>B</italic>} <italic>T/(κL</italic> ^{<italic>2</italic>} <italic>)</italic> , that measures the softness of a functional coordinate relative to thermal noise, and show that resolving each machine into its collective-mode spectrum {γα} separates structural from functional degrees of freedom in a way that resolves internal inconsistencies of single-parameter analyses. Building on this mode decomposition, we derive the permachine capacity <italic>U</italic> _{<italic>max</italic>} and the per-event update energy <italic>E</italic> _{<italic>up</italic>} from a coupled harmonic Hamiltonian, and define a dimensionless retention burden <italic>R</italic> = <italic>P</italic> _{<italic>maintτret</italic>} <italic>/(u</italic> _{<italic>write</italic>} <italic>k</italic> _{<italic>B</italic>} <italic>T )</italic> that quantifies the excess cost of active storage above the Landauer floor. Applied to the ribosome, the Na ⁺ /K ⁺ -ATPase, and the hippocampal synapse, the framework recovers direct force and energy measurements without adjustable parameters and predicts a two-mode architecture for persistent memory. In the synaptic case, the mode-decomposed Shannon capacity reduces to the biophysical scaling <italic>σ</italic> ⁻² ∝ <italic>E</italic> ⁵ reported by Malkin and coworkers and reproduces the efficiency-versus- conductance data of Harris et al. under the mapping given by Stone. Three empirical predictions follow: a stiffness ratio <italic>κ</italic> _{<italic>R</italic>} <italic>/κ</italic> _{<italic>A</italic>} set by the log-ratio of retention and adaptation timescales, an actin/scaffold transfer coefficient ζ ∼ 0.1–0.3 testable by cofilin inhibition, and a system-independent scaling of R with write rate across biological memory substrates. </p>