Landauer cost in a continuous vacuum/no-vacuum measurement

TL;DR

The paper analyzes the thermodynamic cost of continuously monitoring a bosonic mode to decide vacuum versus non-vacuum, treating the measurement as a time-binned binary record that is erased after each bin. It shows that the minimal dissipated heat per bin is bounded by Landauer's principle as $Q_{\min}^{(1)}(t) \ge \frac{k_B T}{\tau} H_2(P_\tau)$, with $P_\tau = 1 - e^{ -\gamma(1-p_0(t))\tau }$, and generalizes to $N$ modes via the joint entropy $H(\mathbf{Y}_t)$. It discusses how coarse-graining, correlations, and mode density control the actual cost and provides circuit-QED parameter estimates, plus a speculative horizon-based thought experiment linking information throughput to cosmological scales. The significance is that the thermodynamic footprint of continuous quantum measurements arises from information processing (throughput and compressibility) rather than the energy of the measured mode, offering a concrete bridge between measurement theory, information theory, and thermodynamics.

Abstract

We study the thermodynamic cost of maintaining a continuous binary record of a vacuum or no-vacuum measurement. Modeling the monitoring as a time-binned click or no-click process with finite bandwidth, we treat the outcomes as a classical register that is reset after each bin. Landauer's principle then yields an operational lower bound on the dissipated heat rate set by the Shannon entropy rate of the measurement record. We discuss the role of coarse-graining, extend the analysis to many monitored modes, including correlations and compressibility, and provide parameter estimates for circuit-QED photon monitoring, with a speculative horizon-based bookkeeping illustration.

Figures (1)

• Figure 1: Record entropy per bin as a function of non-vacuum probability, once the product $\gamma \tau$ is fixed.