Thermodynamics is useful because it lets us predict and control complex systems from a few accessible quantities when microscopic reconstruction is impractical. We ask whether this operational reduction can be less costly in a finite quantum system than in a matched classical one. We compare a few-boson Bose--Hubbard chain with its number-conserving classical-field counterpart under the same driving and the same coarse spatial record. The quantum system relaxes more in the observed particle distribution, yet the retained mean energy resolves more of the microscopic structure hidden by that record, leaving less information unusable and smaller entropy generation. We then close the process into a heat-engine cycle whose controls use only the measured mean energy and spatial record, not full state tomography; at matched thermal resources, the smaller entropy generation gives more work and higher efficiency. The advantage fades as the particle number grows toward the classical-field regime.
Thermodynamics is useful because it lets us predict and control complex systems from a few accessible quantities when microscopic reconstruction is impractical. We ask whether this operational reduction can be less costly in a finite quantum system than in a matched classical one. We compare a few-boson Bose--Hubbard chain with its number-conserving classical-field counterpart under the same driving and the same coarse spatial record. The quantum system relaxes more in the observed particle distribution, yet the retained mean energy resolves more of the microscopic structure hidden by that record, leaving less information unusable and smaller entropy generation. We then close the process into a heat-engine cycle whose controls use only the measured mean energy and spatial record, not full state tomography; at matched thermal resources, the smaller entropy generation gives more work and higher efficiency. The advantage fades as the particle number grows toward the classical-field regime.
A useful thermodynamic model predicts what a device will do without tracking its full microscopic state. For a finite quantum working medium, the difficult question is which quantities should actually be measured. We develop a task-based method that keeps exact energy accounting separate from calibrated macroscopic prediction. Operator geometry identifies what a measured record determines and bounds what remains uncertain. We then compare direct measurements of dynamical observables with earlier measurements of the same coarse record, selecting the representation together with its measurement cost. A Bose--Hubbard example yields a compact response table tested over a continuous operating region and on unseen microscopic trajectories. A driven Ising chain shows why history is not always the cheaper choice. The result is a way to turn detailed quantum dynamics into a small, reusable, and explicitly qualified thermodynamic description.
We study the modification of the second law of thermodynamics for a quantum system interacting with a reservoir regarding quantum coherence. The whole system is isolated so that neither energy nor information is lost. It is discovered that the coherence of the reservoir can serves as a useful resource allowing the system extract more energy from the reservoir; among the coherence measures, only is the relative entropy of coherence feasible to quantitatively characterize energy exchange. We demonstrate that a thermodynamic cycle between two coherent reservoirs can output more work than its classical counterpart. The efficiency of such cycle surpasses the Carnot efficiency, which is the upper bound of heat engine efficiency in classical regime.
Microscopic unitary dynamics preserves all fine information, yet an isolated finite system can show a robust thermodynamic window in which the entropy associated with a restricted record rises. We ask why information hidden from the current record usually fails to rebuild a low-entropy macrostate. For a fixed projective record, every finite step separates exactly into the evolution predicted from the record alone and an exact correction carried by unresolved microscopic structure. The record-only contribution starts only at second order in time, so all instantaneous change of the record comes from hidden currents between macrostates. We derive the exact entropy rate, separate entropy-spreading from return-oriented currents, and resolve those currents into energy-gap amplitudes. Transitions with the same gap add coherently, revealing how the Hamiltonian and the microscopic state organize hidden information for return. In interacting mixing dynamics the current power is spread over many frequencies; free and deliberately commensurate controls progressively concentrate it, and the engineered dynamics reconstructs a low-entropy macrostate. An independent distribution-level test separates hidden dynamical activity from finite-step return, and an exact classical measure-preserving counterpart shows which parts of the construction are not uniquely quantum. Within the specified record and observation window, irreversibility is therefore not loss of microscopic information, but the failure of that information to organize currents that restore macroscopic order.
Thermodynamics is one of the main pillars of theoretical physics, and it has a special appeal of having wide applicability to a large variety of different physical systems. However, many assumptions in thermodynamics apply only to systems which are bulk material, i.e. consisting a large number of microscopic classical particles. Due to the advancement of designing nanoscale engines, especially in the light of devices that are used today in the processing of quantum information, is thermodynamics still applicable? Can we refine the core principles of thermodynamics to suit such nanoscale quantum systems as well? The central aim of this thesis is to construct a theory of thermodynamics that holds for nanoscale quantum systems, even those as small and simple as a single qubit. We do this by starting out from the core basics of quantum theory: unitary dynamics on closed quantum systems. We adapt a resource theoretic approach inspired by quantum information theory, which defines the quantum states and operations allowed to be used in a thermodynamic evolution. With this framework that naturally adopts the first law as an energy preserving condition, we show the refinement of both the zeroeth and second law of thermodynamics. The zeroeth law explains the physical significance of the Gibbs thermal state. On the other hand, we show that the second law sees refinement in the quantum nanoregime: instead of having the free energy as the sole quantity dictating the possibility of a thermodynamic state transition, we derive a family of generalized free energies that also constitute necessary conditions for a transition to occur. Moreover, these conditions become sufficient for states which are block-diagonal in the energy eigenbasis. In this thesis, we also brought our approach of thermodynamics to the next step: we apply our findings on the second laws, in order to analyze the maximum achievable efficiency for quantum heat engines. In classical thermodynamics, the Carnot efficiency has been long known as the theoretical maximum which does not depend on the specific structure of the thermal baths used, but only on its temperature. With the additional free energies we discover, we show that although quantum heat engines may achieve the Carnot efficiency, such an achievability is no longer independent of the Hamiltonians of the thermal baths. In other words, we find additional restrictions that surface in the study of quantum nanoscale heat engines, which are a direct consequence of the generalized second laws. This has provided us with a deeper understanding into the fundamental limitations of how efficient devices can be made in the realm of microscopic quantum systems.
In classical thermodynamic processes the unavoidable presence of irreversibility, quantified by the entropy production, carries two energetic footprints: the reduction of extractable work from the optimal, reversible case, and the generation of a surplus of heat that is irreversibly dissipated to the environment. Recently it has been shown that in the quantum regime an additional quantum irreversibility occurs that is linked to decoherence into the energy basis. Here we employ quantum trajectories to construct distributions for classical heat and quantum heat exchanges, and show that the heat footprint of quantum irreversibility differs markedly from the classical case. We also quantify how quantum irreversibility reduces the amount of work that can be extracted from a state with coherences. Our results show that decoherence leads to both entropic and energetic footprints which both play an important role in the optimization of controlled quantum operations at low temperature. In classical thermodynamics irreversibility occurs whenever a non-thermal system is brought into contact with a thermal environment. Using quantum trajectories the authors here establish two energetic footprints of quantum irreversible processes, and find that while quantum irreversibility leads to the occurrence of a quantum heat and a reduction of work production, the two are not linked in the same manner as the classical laws of thermodynamics would dictate.
Irreversibility has a fundamental thermodynamic cost, erasing information inevitably generates heat. This connection is quantified by the Landauer bound, which gives the minimum dissipation needed to erase a single bit of information. While this bound applies in both classical and quantum settings, it is saturated only in idealised limits of infinite resources. Here, we provide a unified first principles description of finite-resource erasure in both classical and quantum systems. We begin by proving the communal folklore that in the idealised regime the erasure cost of a bit encoded in a quantum or classical system is the same. Despite this, we show that their practical implementation differs substantially: achieving comparable erasure quality in quantum systems requires more control, larger accessible energy gaps and longer operation times. Classical protocols can achieve the erasure of a comparable quantum protocol under far weaker constraints which we expose in trade-off relations. Our results explain why practical erasure schemes fall short of Landauer's bound and show that classical systems enjoy several fundamental thermodynamic advantages.