The thermodynamics of readout devices and semiclassical gravity

TL;DR

This work investigates whether nonlinear extensions of quantum theory that include readout devices can violate the second law of thermodynamics, using Møller–Rosenfeld semiclassical gravity as a primary example. It introduces measurement entropy as the appropriate thermodynamic quantity in readout-device worlds and analyzes classic no-go arguments (Peres, von Neumann, Hänggi–Wehner) under this framework. The authors show that, once RD-appropriate entropy accounting and energy costs of information processing are included, these arguments do not entail a second-law violation; in particular, semiclassical gravity can be thermodynamically consistent. The results suggest that nonlinear quantum extensions with readout devices do not generically conflict with thermodynamics, reinforcing the viability of semiclassical gravity regimes under a careful information-theoretic lens with potential implications for foundational physics and quantum gravity approximations.

Abstract

We analyse the common claim that nonlinear modifications of quantum theory necessarily violate the second law of thermodynamics. We focus on hypothetical extensions of quantum theory that contain readout devices. These black boxes provide a classical description of quantum states without perturbing them. They allow quantum state cloning, though in a way consistent with the relativistic no-signalling principle. We review the existence of such devices in the context of Moller-Rosenfeld semiclassical gravity, which postulates that the gravitational field remains classical and is sourced by the expectation value of a quantum energy-momentum tensor. We show that the definition of information in the models examined in this paper deviates from that given by von Neumann entropy, and that claims of second law violations based on the distinguishability of non-orthogonal states or on violations of uncertainty principles fail to hold in such theories.

Figures (3)

• Figure 1: Cycle extracting heat from an isothermal reservoir and converting it into work using a semi-permeable non-quantum membrane that separates a specific pair of non-orthogonal states as well as a semi-permeable quantum membrane that separates a specific pair of orthogonal states. The quantum membranes, which let through one of two orthogonal states, are depicted as solid double lines, while the semi-permeable membranes, which can be implemented by readout devices and let through one of two non-orthogonal states, are shown in dashed double lines. Walls, which do not let any states through, are depicted with single lines.
• Figure 2: Quantum measurements as a black box in RD world. A possible model of quantum measurements in this post-quantum setting is as a composite process of (i) an RD capturing the information of the input state and placing it in some register (perhaps within the measurement apparatus), (ii) the quantum instrument $\mathcal{I}(\cdot)$ associated to the quantum measurement, applying the non-selective quantum operation, and (iii) a random number generator (RNG), selecting one specific outcome at random.
• Figure 3: The Hänggi-Wehner cycle which can extract net work if the uncertainty principle is violated and other principles are left unchanged. As discussed in the text, this cycle fails to extract net work for the nonlinear models we consider. First (a) the system is prepared in two states $\rho_1$ and $\rho_2$ in separated volumes, each with $N/2$ particles. (b) We then replace the wall by semi-transparent membranes that let through one state but block the other. (c) These membranes move apart until equilibrium $\rho$ is reached. (d) Insert new membranes to separate the pure components of $\rho$. (e) Subdivide these into smaller regions such that the resulting pure states are building blocks of $\rho_1$ and $\rho_2$. (f) Unitarily transform these states into the pure state decomposition of $\rho_1$ and $\rho_2$