Here we demonstrate how the interplay between quantum coherences and a decoherence bath, such as one given by continuos quantum measurements, lead to new kinds of thermodynamic potentials and flows. We show how a mathematical extension of thermodynamics includes decoherence baths leading to a more general sense of the zeroth and first law. We also show how decoherence adds contributions to the change in entropy production in the second law. We derive a thermodynamic potential that depends only on the interplay between quantum coherences and a decoherence thermodynamic bath. This leads to novel thermodynamic effects, such as Onsager relationships that depend on quantum coherences. This provides a thermodynamics interpretation of the role of decoherence on quantum transport in very general systems.
Here we demonstrate how the interplay between quantum coherences and a decoherence bath, such as one given by continuos quantum measurements, lead to new kinds of thermodynamic potentials and flows. We show how a mathematical extension of thermodynamics includes decoherence baths leading to a more general sense of the zeroth and first law. We also show how decoherence adds contributions to the change in entropy production in the second law. We derive a thermodynamic potential that depends only on the interplay between quantum coherences and a decoherence thermodynamic bath. This leads to novel thermodynamic effects, such as Onsager relationships that depend on quantum coherences. This provides a thermodynamics interpretation of the role of decoherence on quantum transport in very general systems.
Quantum decoherence is seen as an undesired source of irreversibility that destroys quantum resources. Quantum coherences seem to be a property that vanishes at thermodynamic equilibrium. Away from equilibrium, quantum coherences challenge the classical notions of a thermodynamic bath in a Carnot engines, affect the efficiency of quantum transport, lead to violations of Fourier's law, and can be used to dynamically control the temperature of a state. However, the role of quantum coherence in thermodynamics is not fully understood. Here we show that the relative entropy of a state with quantum coherence with respect to its decohered state captures its deviation from thermodynamic equilibrium. As a result, changes in quantum coherence can lead to a heat flow with no associated temperature, and affect the entropy production rate. From this, we derive a quantum version of the Onsager reciprocal relations that shows that there is a reciprocal relation between thermodynamic forces from coherence and quantum transport. Quantum decoherence can be useful and offers new possibilities of thermodynamic control for quantum transport.
A central open question in quantum thermodynamics is the identification of thermodynamic entropy away from equilibrium. Although thermodynamic entropy coincides with the von Neumann entropy for a Gibbs state at equilibrium, the thermodynamic role of quantum coherence generated during nonequilibrium evolution remains unclear. Here, we show that von Neumann entropy does not, in general, represent the thermodynamic entropy governing heat exchange in coherent nonequilibrium quantum systems. By integrating the resource theory of quantum coherence with thermodynamic principles, we develop a general framework for nonequilibrium quantum thermodynamics. We identify thermodynamic entropy with the energy entropy derived from energy-measurement statistics and introduce a dynamical temperature extending the equilibrium concept to nonequilibrium states. Consequently, we obtain an exact entropy-balance relation separating the entropy flux associated with heat exchange from the coherence-loss contribution to entropy production, establishing an operational connection between quantum coherence, heat flow, and total entropy change. Unlike approaches relying on equilibrium reference states or stationary Gibbs ensembles, our framework uses instantaneous dynamical quantities and remains valid throughout transient nonequilibrium evolution. It provides consistent dynamical definitions of temperature, work, heat, and free energy. Applying the formalism to an exactly solvable open quantum system, we show that the first and second laws hold throughout transient evolution and that equilibrium thermodynamics emerges dynamically in the weak-coupling long-time limit. Our results establish a unified framework for coherent nonequilibrium quantum thermodynamics and suggest opportunities for controlling heat dissipation through coherence engineering in quantum thermal technologies.
The first half of this thesis is dedicated to the study of generalizations of probability theory which include quantum theory and many of its alternatives. This research program seeks to understand quantum theory by exploring it ‘from the outside’, where it sits within a landscape of all operationally defined theories. We approach this problem with a new perspective: generalized decoherence. Quantum theory recovers classical theory via decoherence, where a ‘classical limit’ is achieved by a quantum system interacting with its environment, losing its quantum coherence. Typically it is the emergence of the classical world from the quantum that is studied. We reverse this paradigm and ask - how does the existence of a classical limit define the structure of quantum theory, or any other post-classical theory? We derive the existence of entangled states as a necessary feature of any theory that allows for the emergence of the classical world in this way. We then use our framework for generalized decoherence to explore the properties of theories that can ‘hyperdecohere’ to quantum theory. We find that any such theory must be very exotic compared to quantum theory, violating either the postulate of tomographic locality, reversibility, causality or purity. In the second half of this thesis we turn our attention to the second law of thermodynamics. We present a framework for deriving the second law under general constraints and explore two pertinent examples, constraining the fluctuations in work and constraining the size of the thermal bath and deriving the second law in these cases. Bounding fluctuations results in a unified free energy that contains the single-shot and Helmholtz free energies as limiting cases. Bounding the size of the thermal bath results in a finite-bath second law that is more general that previous attempts and draws connections between non-asymptotic thermodynamics and second-order information theory.
In quantum thermodynamics, the decomposition of energy exchanges into heat and work remains an open problem beyond weak-coupling and slow-driving regimes. Recent formulations have shown that quantum coherence introduces additional energy contributions whose thermodynamic interpretation is still under debate, raising fundamental questions about the structure of the quantum first law. In this work, we investigate this problem through a time-dependent perturbative framework applied to the first law of quantum thermodynamics. By expanding the thermodynamic quantities up to second order, we derive explicit perturbative corrections for work, heat, and coherence contributions. Our results show that the coherence term can be consistently decomposed into coherent heat and coherent work, demonstrating that quantum coherence does not require the introduction of an independent energetic contribution beyond heat and work. The formalism resolves inconsistencies associated with previous formulations of the quantum first law, including the interpretation of coherence contributions and their connection with entropy fluxes. At second order, the perturbative corrections become directly connected to transition rates governed by Fermi's golden rule, establishing a bridge between microscopic quantum transitions and macroscopic thermodynamic quantities. These results provide a physically transparent framework to investigate coherence-driven thermodynamic processes and offer new perspectives for the analysis of driven quantum systems and nonequilibrium quantum technologies.
In conventional thermodynamics, a macroscopic process is characterized by changes in thermodynamic variables such as temperature, pressure, and entropy. In quantum thermodynamics, the state of a system is described by a density operator ρ, and the entropy of the system is given by the von Neumann entropy S = -k_B Tr(ρ ln ρ). Recent theoretical investigations have suggested that quantum coherence and phase correlations can also be thermodynamically relevant. This paper introduces the concept of Quantum Thermodynamic Phase Transfer (QTPT), a formalism that treats the quantum phase φ_T as a thermodynamic variable that can change during a process. We propose a set of postulates that extend the first and second laws of thermodynamics to include a term that accounts for the work associated with changes in φ_T. The framework is illustrated with a simple two–level system coupled to a thermal bath and driven by a time–dependent phase. We derive expressions for the generalized free energy and the entropy production that include phase contributions. The implications of QTPT for quantum heat engines, quantum refrigeration, and the fundamental limits of quantum thermodynamic cycles are discussed. The potential for a Nobel–level recognition of the unification of quantum coherence with classical thermodynamic principles is highlighted.
The entropy production in dissipative processes is the essence of the arrow of time and the second law of thermodynamics. For dissipation of quantum systems, it was recently shown that the entropy production contains indeed two contributions: a classical one and a quantum one. Here we show that for degenerate (or near-degenerate) quantum systems there are additional quantum contributions which, remarkably, can become negative. Furthermore, such negative contributions are related to significant changes in the ongoing thermodynamics. This includes phenomena such as generation of coherences between degenerate energy levels (called horizontal coherences), alteration of energy exchanges, and, last but not least, reversal of the natural convergence of the populations toward the thermal equilibrium state. Going further, we establish a complementarity relation between horizontal coherences and population convergence, which is particularly enlightening for understanding heat flow reversals. Conservation laws of the different types of coherences are derived. Some consequences for thermal machines and resource theory of coherence are suggested.