This paper closes the action–reaction post-quantum series by proposing thermodynamic fluctuations as an intrinsic stabilizer for Sutherland’s back-reaction dynamics. Building on prior work in self-organization, weak values, geometric phase, and torsion bounds, we introduce a deterministic, audit-friendly entropy budget (a “clamp”) that caps probability-flow deviations without requiring an external thermal bath. The cap is set by the model’s own vacuum-fluctuation surrogate already present in the numerical scheme, avoiding a new temperature-like tuning parameter. We clarify connections to fluctuation theorems (Jarzynski/Crooks/Sagawa–Ueda) without claiming new equalities. AI-assisted large-scale simulations (1D, up to 10^6 iterations) show stable localization in harmonic and free-particle cases at scales beyond manual computation, with transparent logs indicating when and how the clamp acted. Standard quantum mechanics emerges in the zero-back-reaction limit (and, when applicable, the zero-noise limit). We outline five falsifiable predictions for trapped-ion and interferometry platforms and give explicit criteria under which the mechanism is constrained or ruled out.
This paper closes the action–reaction post-quantum series by proposing thermodynamic fluctuations as an intrinsic stabilizer for Sutherland’s back-reaction dynamics. Building on prior work in self-organization, weak values, geometric phase, and torsion bounds, we introduce a deterministic, audit-friendly entropy budget (a “clamp”) that caps probability-flow deviations without requiring an external thermal bath. The cap is set by the model’s own vacuum-fluctuation surrogate already present in the numerical scheme, avoiding a new temperature-like tuning parameter. We clarify connections to fluctuation theorems (Jarzynski/Crooks/Sagawa–Ueda) without claiming new equalities. AI-assisted large-scale simulations (1D, up to 10^6 iterations) show stable localization in harmonic and free-particle cases at scales beyond manual computation, with transparent logs indicating when and how the clamp acted. Standard quantum mechanics emerges in the zero-back-reaction limit (and, when applicable, the zero-noise limit). We outline five falsifiable predictions for trapped-ion and interferometry platforms and give explicit criteria under which the mechanism is constrained or ruled out.
How macroscopic, deterministic order emerges from microscopic systems governed by quantum and thermal fluctuations remains a central problem in non-equilibrium statistical mechanics. While classical reaction theories based on linear energy landscapes describe thermally activated processes, they do not fully account for the extreme state localization observed in complex systems such as molecular recognition. Here, we propose the Information-driven Quantum Geometric (IQG) model, a theoretical framework in which measurement-induced feedback modifies the effective free-energy landscape. By combining coarse-grained quantum dynamics with large deviation theory, we show that nonlinear information feedback induces a sharp geometric crossover—termed the Fidelity Cliff—marking a transition from fluctuation-dominated dynamics to deterministic state locking. Numerical analysis based on a nonlinear Fokker-Planck equation demonstrates the formation of a noise-suppressed metastable subspace (NSMS), where an emergent energy gap provides spectral protection against environmental noise. This mechanism ensures robust state localization despite continuous thermal perturbations. Our results establish a unified physical framework linking quantum measurement dynamics to classical reaction kinetics, providing a quantitatively testable mechanism for the emergence of macroscopic attractors in dissipative systems.
To understand in detail the relation between unitary quantum theory that describes our world at the microscopic scale and thermodynamics, which was long believed only to apply to macroscopic objects, is one of the most interesting and long-standing problems in physics. Recently, this problem has received renewed attention, in particular from the community of quantum information theory, but also from the field of statistical mechanics, inspired from stochastic thermodynamics. These results suggest that thermodynamics is also relevant for individual quantum systems, provided that they can be brought into contact with thermal baths. In this thesis, I use recently developed tools to provide new results both on fundamental questions, but also on questions which are of practical relevance for potential miniaturized thermal machines. In terms of fundamental questions, the results in this thesis contribute to understanding how the basic laws of thermodynamics and statistical mechanics can be understood directly from unitary quantum mechanics. In particular, I discuss and answer the following questions: i) How can we quantify the third law of thermodynamics using information theoretic methods? ii) How can we quantify the "thermodynamic value" of a state-transition in quantum systems? iii) How can we axiomatically characterize the non-equilibrium free energy and relative entropy? iv) How can we justify statistical ensembles from an operational perspective, without having to introduce either some probability measures or an information theoretic entropy measure? v) How can we understand the equilibration of closed quantum systems, how long does it take and how difficult is it to avoid? In the second part of the thesis I discuss in detail how experimental restrictions, which become important at the quantum scale, influence the ultimate thermodynamic bounds for thermal machines. In particular, the results in this thesis provide thermodynamic bounds on work-extraction and efficiencies of thermal machines in situations where 1.) an experimenter only has limited field strengths available, 2.) an experimenter cannot control the interactions between particles, but external fields arbitrarily well, and 3.) situations in which a small quantum system can only be strongly coupled to heat baths. These bounds are tight and I provide explicit examples illustrating the different behaviours. Finally, I come back to a classic problem in statistical physics: The emergence of spontaneous symmetry breaking. Here, I provide general and rigorous new results that show how symmetry-breaking stationary states emerge from fluctuations in order parameters in dissipative lattice models.
We study the back-reaction of quantum systems onto classical ones. Taking the starting point that semi-classical physics should be described at all times by a point in classical phase space and a quantum state in Hilbert space, we consider an unravelling approach, describing the system in terms of a classical-quantum trajectory. We derive the general form of the dynamics under the assumptions that the classical trajectories are continuous and the evolution is autonomous, and the requirement that the dynamics is linear and completely positive in the combined classical-quantum state. This requirement is necessary in order to consistently describe probabilities, and forces the dynamics to be stochastic when the back-reaction is non-zero. The resulting equations of motion are natural generalisations of the standard semi-classical equations of motion, but since the resulting dynamics is linear in the combined classical-quantum state, it does not lead to the pathologies which usually follow from evolution laws based on expectation values. In particular, the evolution laws we present account for correlations between the classical and quantum system, which resolves issues associated with other semi-classical approaches. In addition, despite a breakdown of predictability in the classical degrees of freedom, the quantum state evolves deterministically conditioned on the classical trajectory, provided a trade-off between decoherence and diffusion is saturated. As a result, the quantum state remains pure when conditioned on the classical trajectory. To illustrate these points, we numerically simulate a number of semi-classical toy models, including one of vacuum fluctuations as a source driving the expansion of the universe. Finally, we discuss the application of these results to semi-classical gravity, and the black-hole information problem.
We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that for a specific class of generalized measurements, which include projective measurements, unitality replaces microreversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.
Thermodynamics is a phenomenological theory describing the energy conversion of work and heat. At its origins thermodynamics was developed in order to understand and improve heat engines. In conventional thermodynamics, however, only such processes are completely describable which are slow enough to keep the system of interest in an equilibrium state with its thermal environment at all times. On the contrary, all real physical processes are accompanied by non-equilibrium phenomena. These are mathematically described with the help of the irreversible entropy production, i.e. the dissipated work divided by the temperature of the bath. The second law of thermodynamics merely states that the irreversible entropy production is on average always positive. The modern trend of miniaturization, however, leads to smaller and smaller devices. On short length scales thermal noise as well as quantum fluctuations become important. Thus, usual thermodynamic quantities as work and heat acquire stochastic nature. Moreover, in the quantum regime a completely new theory had to be invented, since classical notions of work and heat are no longer valid. The present dissertation contributes to this prevailing field by the derivation of analytical expressions for the entropy production in open and closed quantum system far from thermal equilibrium. The theoretical treatment is motivated by an experimental point of view. The obtained results were derived from the reduced dynamics of the quantum mechanical system, which may be coupled to a thermal bath. To this end, it was dealt with methods and approaches of statistical physics, conventional thermodynamics, quantum information theory and the theory of open quantum systems. In this dissertation the most important physical systems are treated. First, an isolated system is considered before later on a heat bath is included. The limit of weak as well as of strong coupling are analyzed in detail. For isolated systems it turns out that a geometric approach is able to capture the thermodynamic properties, completely. To this end, the irreversible entropy production is sharply estimated from below by the angle between the real non-equilibrium state and the corresponding equilibrium one. Further, it is shown that the Heisenberg uncertainty relation for energy and time can be formulated more precisely in terms of that angle. As experimental system cold ion traps are introduced, in which the theoretical predictions can be verified. For weakly coupled systems, then, the irreversible entropy production is identified and a fluctuation theorem is derived by merely thermodynamic arguments. As experimental system we, again, propose the cold ion traps, where the heat bath can be simulated with the help of LASER light. In the limit of strong coupling a semiclassical description of the reduced quantum system is discussed. Again, an analytically exact expression for the entropy production and the corresponding fluctuation theorem is derived. A physical system, in which strong coupling to the environment can be analyzed, is given by Josephson junctions. This dissertation discusses the entropy production for isolated, weakly coupled, and overdamped quantum systems. For these physical regimes analytical relation are derived and experimental systems proposed, with which the predictions can be verified.
We present a deterministic extension of de Broglie-Bohm pilot-wave theory that resolves the fundamental action-reaction asymmetry of the standard formulation. By introducing a reciprocal coupling term sourced by the imaginary part of the momentum weak value, Im(pw) = -(ħ/2)∇ ln ρ, we enable the particle configuration to influence the guiding wavefunction locally. To prevent the anti-diffusive instabilities inherent in such back-reaction models, we introduce a parameter-free "Fluctuation Clamp" mechanism. This mechanism budgets allowed gradient sharpening against a numerical vacuum surrogate scale, ensuring stability over 10^5 simulation steps while preserving time-symmetry and normalization. The model recovers standard quantum mechanics in equilibrium (ρ = |ψ|²) and in the weak-coupling limit (λ → 0), but predicts falsifiable deviations in non-equilibrium regimes, specifically in neutron interferometry (velocity shifts Δv ~ 5 × 10^-3 m/s) and tunneling time measurements (dwell time shifts δτ/τ ~ 0.1).