Time evolution operator in quantum mechanics can be changed into a statistical operator by a Wick rotation. This strict relation between statistical mechanics and quantum evolution can reveal deep results when the thermodynamic limit is considered. These results translate in a set of theorems proving that these effects can be effectively at work producing an emerging classical world without recurring to any external entity that in some cases cannot be properly defined. In a many-body system has been recently shown that Gaussian decay of the coherence is the rule with a duration of recurrence more and more small as the number of particles increases. This effect has been observed experimentally. More generally, a theorem about coherence of bulk matter can be proved. All this takes us to the conclusion that a well definite boundary for the quantum to classical world does exist and that can be drawn by the thermodynamic limit, extending in this way the deep link between statistical mechanics and quantum evolution to a high degree.
Time evolution operator in quantum mechanics can be changed into a statistical operator by a Wick rotation. This strict relation between statistical mechanics and quantum evolution can reveal deep results when the thermodynamic limit is considered. These results translate in a set of theorems proving that these effects can be effectively at work producing an emerging classical world without recurring to any external entity that in some cases cannot be properly defined. In a many-body system has been recently shown that Gaussian decay of the coherence is the rule with a duration of recurrence more and more small as the number of particles increases. This effect has been observed experimentally. More generally, a theorem about coherence of bulk matter can be proved. All this takes us to the conclusion that a well definite boundary for the quantum to classical world does exist and that can be drawn by the thermodynamic limit, extending in this way the deep link between statistical mechanics and quantum evolution to a high degree.
Time evolution operator in quantum mechanics can be changed into a statistical operator by a Wick rotation. This strict relation between statistical mechanics and quantum evolution can reveal deep results when the thermodynamic limit is considered. These results translate in a set of theorems proving that these effects can be effectively at work producing an emerging classical world without recurring to any external entity that in some cases cannot be properly defined. For a many-body system it has been recently shown that Gaussian decay of the coherence is the rule with a duration of recurrence more and more small as the number of particles increases. This effect has been observed experimentally. More generally, a theorem about coherence of bulk matter can be proved. All this takes us to the conclusion that a well defined boundary for the quantum to classical world does exist and that can be drawn by the thermodynamic limit, extending in this way the deep link between statistical mechanics and quantum evolution to a high degree.
We prove a very general theorem on decoherence in the thermodynamic limit, widely extending the scope of our preceding results [Phys. Lett. A 308, 135 (2003)]. The concept of a singular limit in time is used in the proof. Recent experimental findings [1, 2, 3, 4, 5] in NMR with organic molecular crystals have shown that an intrinsic decoherence effect is present in a many-body system in the thermodynamic limit. These experiments, that are known just in the NMR community, give a strong support to our understanding of decoherence as an effect arising from the thermodynamic limit applied to unitary evolution [6, 7, 8, 9, 10, 11, 12]. These theoretical results are based on a concept of singular limit in time. This concept seems to have been pioneered by Bohm [13, 14]. Indeed, the existence of such an effect would give a relevant answer both to the measurement problem and the question of the irreversibility: both are essential to the understanding of a classical world emerging from quantum mechanics. Besides, recent experiments with cavities realized by Haroche’s group [15, 16] have produced asymptotic states with a large number of photons as foreseen by Gea-Banacloche [17, 18] and further analyzed by Knight and Phoenix [19, 20]. As firstly pointed out by Gea-Banacloche, these states support a view of quantum measurement described by decoherence in the thermodynamic limit, in agreement with our view. In this case one has that
At present there is a consensus about the fact that the emergence of the classical world from the underlying quantum reality involves the physical phenomenon of decoherence, which is usually studied in the version proposed by Zurek and his collaborators. According to this version, decoherence is a process resulting from the interaction between a quantum system and its environment (environment-induced decoherence, EID); this process singles out the observables that receive definite classical values. The aim of this paper is to propose a top-down approach to decoherence, which takes the perspective of the whole closed system, and considers whether each set of degrees of freedom decoheres or not. This approach is more general than the orthodox open-system perspective and dissolves some of its conceptual problems. Although decoherence becomes relative to the way in which the closed system is decomposed, the quantum-to-classical transition defines unequivocally the realm of classicality by identifying the observables with classical-like behavior.
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.
Starting from the thermodynamic limit of information recording, this paper derives a complete, universal decoherence formula consisting of three linked equations: 1. A **non-zero lower bound on the decoherence time** of a quantum system: `τ_min = (ℏ / k_B T) · (1 / ln N_eff)`, where `N_eff` is the number of effective environmental degrees of freedom participating in the irreversible recording of the system's information. 2. A **quantitative criterion for the macroscopic–microscopic boundary**: `N_eff^(c) = exp( ℏ / (k_B T · T_sys) )`, where `T_sys` is the characteristic evolution time of the system. When `N_eff > N_eff^(c)`, decoherence completes before a single coherent evolution, and classical behavior emerges. 3. A **thermodynamic lower bound on interference fringe visibility**: `V ≥ exp( − ln N_eff / ln N_eff^(c) )`, derived from the first two equations without additional assumptions. The first equation predicts a *saturation effect*: the decoherence time no longer shortens indefinitely as environmental coupling increases. The second shows that for nearly all laboratory-accessible systems, `N_eff^(c) ≈ 1`, meaning any non-zero environmental coupling suffices to trigger the transition—explaining why macroscopic objects are inevitably classical. The third provides a directly measurable observable for the continuous quantum–classical phase transition. The framework is universal, applies to any quantum system in contact with an environment at temperature `T`, and its three core predictions are independently falsifiable. Based on the boundary criterion, wave–particle duality in double-slit experiments is reinterpreted as a special case of this phase transition occurring under the limiting condition `N_eff^(c) ≈ 1`. Three experimental schemes—a decoherence-saturation ratio test, a temperature-dependence test of the boundary criterion, and a direct observation of the continuous wave–particle transition via ultrafast electron diffraction or circuit QED—are proposed, all feasible on existing quantum information platforms without requiring new equipment.
Environment induced decoherence [1] has taught us that unitary evolution can be very fragile. Recent experiments with cavities [2], ion traps [3] and interference [4] confirm this expectation. All the experiments carried out so far do not help to answer a fundamental question: Can we maintain unitary evolution down to the Planck time? Different formulations of intrinsic decoherence [5-9] foresee that effects on smaller scales permit us to understand the breaking of the unitary evolution and in some way point out possible answers to our question. But, one can ask if some experiments in quantum optics can be devised to find an answer to the question with the present technology. Decoherence in the thermodynamic limit is a proposal to respond to these questions assuming that the Planck time should be a boundary between different physical theory, that is, we have a singular limit [10]. This singular limit is due to blurring in time and an experimental device will always introduce an average with its proper timescale. We show, with some examples recently presented in literature [11-15], how quantum optics can help to give a definite answer to the main question about unitary evolution, providing in this way direct hints for new physics. This approach to decoherence appears as a new understanding of the measurement problem in quantum mechanics.