Information-Thermodynamic Analysis of the DNA--RNA Polymerase Complex via Interface Dissipation: Based on Observer--Observed Swap Symmetry

RNA polymerase (RNAP) elongates RNA by walking along a DNA template and selectively incorporating ribonucleoside triphosphates (rNTPs). Rather than mechanically replicating the base sequence, RNAP conditions binding and chemistry on the currently read template nucleotide, converting sequence dependence into a bias in its stochastic motion. Thermal fluctuations generate forward/backward translocation attempts; cognate rNTP binding and incorporation stabilize the forward register and suppress backward return, yielding net advance via a Brownian-ratchet mechanism. We formulate the DNA--RNAP complex as a bipartite stochastic system, separating template-side degrees of freedom $X$ from RNAP-side response degrees of freedom $Y$. Irreversibility is quantified by a Kullback--Leibler divergence between forward and time-reversed path measures, yielding joint and marginal dissipations. From these we define an exchange-invariant interface dissipation $Σ_{\mathrm{int}}$ that isolates time-reversal asymmetry generated specifically by coupling across the DNA--RNAP interface. We prove an exchange-symmetric second law, $Σ_{\mathrm{int}}\ge 0$, and show that this interface measure is well defined without invoking local detailed balance. To connect the framework to data analysis, we present a minimal continuous-time Markov jump model implementing the Brownian-ratchet logic and a likelihood-ratio protocol to estimate dissipation rates from discretely sampled trajectories. Finite-sample convergence is assessed via Markov-order diagnostics, clarifying bias--variance tradeoffs under coarse-graining. The interface-centered measure provides a consistent basis for comparing energetic cost across regimes (sequence-dependent kinetics, misincorporation, backtracking, proofreading) and can be combined with hidden-state inference when internal states are partially observed.