A model computational quantum thermodynamic network is constructed with two variable temperature baths coupled by a linker system, with an asymmetry in the coupling of the linker to the two baths. It is found in computational simulations that the baths come to "thermal equilibrium" at different bath energies and temperatures. In a sense, heat is observed to flow from cold to hot. A description is given in which a recently defined quantum entropy S_{univ}^{Q} for a pure state "universe" continues to increase after passing through the classical equilibrium point of equal temperatures, reaching a maximum at the asymmetric equilibrium. Thus, a second law account ΔS_{univ}^{Q}≥0 holds for the asymmetric quantum process. In contrast, a von Neumann entropy description fails to uphold the entropy law, with a maximum near when the two temperatures are equal, then a decrease ΔS^{vN}<0 on the way to the asymmetric equilibrium.
A model computational quantum thermodynamic network is constructed with two variable temperature baths coupled by a linker system, with an asymmetry in the coupling of the linker to the two baths. It is found in computational simulations that the baths come to "thermal equilibrium" at different bath energies and temperatures. In a sense, heat is observed to flow from cold to hot. A description is given in which a recently defined quantum entropy S_{univ}^{Q} for a pure state "universe" continues to increase after passing through the classical equilibrium point of equal temperatures, reaching a maximum at the asymmetric equilibrium. Thus, a second law account ΔS_{univ}^{Q}≥0 holds for the asymmetric quantum process. In contrast, a von Neumann entropy description fails to uphold the entropy law, with a maximum near when the two temperatures are equal, then a decrease ΔS^{vN}<0 on the way to the asymmetric equilibrium.
Recent theoretical and experimental work on the foundations of statistical mechanics and thermodynamics has shown that quantum pure states typically evolve to thermal equilibrium. We focus on formulating the second law of thermodynamics for these states. The standard quantum von Neumann quantum entropy is constant during equilibration, S^{vN}=0, in apparent conflict with the entropy increase of the second law, ΔS_{univ} > 0. We explore a recently developed entropy S_{univ}^Q for a pure state and test its behavior in simulations of a model system and environment evolving in time with heat flow to equilibrium. We find that the entropy approaches the correct classical value in a type of classical limit with weak coupling. With stronger coupling, we find a new source of quantum "excess entropy production," which has its origin in the quantum spreading of the wavepacket. Are there quantum thermodynamic effects related to this new source of entropy? To test this, we developed a model for a small variable temperature quantum oscillator bath. We performed simulations where two small baths are linked by a system, with unequal couplings to the baths. The model evolves to a novel type of equilibrium state with unequal temperatures in the baths, with heat flow from cold to hot along the path to equilibrium. We give an account of this behavior in terms of the second law with the quantum entropy S_{univ}^Q. The new formulation of the second law thus appears well-founded and fruitful, with surprising new quantum thermodynamic effects that may still be awaiting discovery, for example in molecules or systems far from equilibrium. \n\nThis dissertation includes previously published and unpublished co-authored material.
The zeroth law of thermodynamics involves a transitivity relation (pairwise between three objects) expressed either in terms of ``equal temperature'' (ET), or ``in equilibrium'' (EQ) conditions. In conventional thermodynamics conditional on vanishingly weak system-bath coupling these two conditions are commonly regarded as equivalent. In this work we show that for thermodynamics at strong coupling they are inequivalent: namely, two systems can be in equilibrium and yet have different effective temperatures. A recent result [J.-T. Hsiang and B. L. Hu, Phys. Rev. D 103, 065001 (2021) for Gaussian quantum systems shows that an effective temperature T∗ can be defined at all times during a system's nonequilibrium evolution, but because of the inclusion of interaction energy, after equilibration the system's T∗ is slightly higher than the bath temperature TB, with the deviation depending on the coupling. A second object coupled with a different strength with an identical bath at temperature TB will not have the same equilibrated temperature as the first object. Thus $ET\ensuremath{\ne}EQ$ for strong coupling thermodynamics. We then investigate the conditions for dynamical equilibration for two objects 1 and 2 strongly coupled with a common bath B, each with a different equilibrated effective temperature. We show this is possible, and prove the existence of a generalized fluctuation-dissipation relation under this configuration. This affirms that in equilibrium is a valid and perhaps more fundamental notion which the zeroth law for quantum thermodynamics at strong coupling should be based on. Only when the system-bath coupling becomes vanishingly weak that ``temperature'' appearing in thermodynamic relations becomes universally defined and makes better physical sense.
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.
We consider a situation where an N-level system (NLS) is coupled successively to two heat baths with different temperatures without being necessarily thermalized and approaches a steady state. For this situation we apply a general Jarzinski-type equation and conclude that heat and entropy is flowing from the hot bath to the cold one. The Clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities. Our approach is illustrated by an analytical example. For the linear regime, i.~e., for small temperature differences between the two heat baths we derive an expression for the heat conduction coefficient.
We construct a finite bath with variable temperature for quantum thermodynamic simulations in which heat flows between a system S and the bath environment E in time evolution of an initial SE pure state. The bath consists of harmonic oscillators that are not necessarily identical. Baths of various numbers of oscillators are considered; a bath with five oscillators is used in the simulations. The bath has a temperaturelike level distribution. This leads to definition of a system-environment microcanonical temperature T_{SE}(t) which varies with time. The quantum state evolves toward an equilibrium state which is thermal-like, but there is significant deviation from the ordinary energy-temperature relation that holds for an infinite quantum bath, e.g., an infinite system of identical oscillators. There are also deviations from the Einstein quantum heat capacity. The temperature of the finite bath is systematically greater for a given energy than the infinite bath temperature, and asymptotically approaches the latter as the number of oscillators increases. It is suggested that realizations of these finite-size effects may be attained in computational and experimental dynamics of small molecules.
Quantum thermodynamics has emerged as a central field for understanding how energy conversion processes occur in microscopic systems. In these systems, effects such as coherence, entanglement, and non-Markovianity play key roles. In this thesis, we explore different ways to describe quantum thermodynamics, using two main approaches: one based on entropy and the other on ergotropy. First, we introduce a generalized approach to quantify non-Markovianity through the breakdown of monotonicity in thermodynamic functions. In this context, the entropy-based heat flow serves as a practical tool to witness and measure quantum memory in unital maps that do not reverse the sign of the internal energy. Next, we analyze the dynamics of ergotropy in open qubits under both Markovian and non-Markovian evolutions. We identify phenomena such as freezing and sudden death of ergotropy, and we establish an analytical relation between the change in ergotropy and the environment-induced work . This provides a clear physical interpretation for the additional term in the first law in the entropy-based formulation. Finally, we propose an ergotropy-based thermodynamic formulation, in which heat is reinterpreted in terms of the change of the passive state associated with the density operator governing the quantum dynamics. This approach allows one to measure non-Markovianity of unital maps more generally and accurately than the entropy-based heat flow. This advantage comes from the direct link between heat and von Neumann entropy, a property ensured by invariance under passive transformations. Moreover, the out-of-equilibrium temperature naturally remains non-negative, similarly to equilibrium thermodynamics.