Thermodynamic Resource Research Articles

Beyond heat baths II: framework for generalized thermodynamic resource theories

Thermodynamics, which describes vast systems, has been reconciled with small scales, relevant to single-molecule experiments, in resource theories. Resource theories have been used to model exchanges of energy and information. Recently, particle exchanges were modeled; and an umbrella family of thermodynamic resource theories was proposed to model diverse baths, interactions, and free energies. This paper motivates and details the family’s structure and prospective applications. How to model electrochemical, gravitational, magnetic, and other thermodynamic systems is explained. Szilárd’s engine and Landauer’s Principle are generalized, as resourcefulness is shown to be convertible not only between information and gravitational energy, but also among diverse degrees of freedom. Extensive variables are associated with quantum operators that might fail to commute, introducing extra nonclassicality into thermodynamic resource theories. An early version of this paper partially motivated the later development of noncommutative thermalization. This generalization expands the theories’ potential for modeling realistic systems with which small-scale statistical mechanics might be tested experimentally.

Quantum Otto engine with exchange coupling in the presence of level degeneracy.

We consider a quasistatic quantum Otto cycle using two effectively two-level systems with degeneracy in the excited state. The systems are coupled through isotropic exchange interaction of strength J>0, in the presence of an external magnetic field B which is varied during the cycle. We prove the positive work condition and show that level degeneracy can act as a thermodynamic resource, so that a larger amount of work can be extracted than in the nondegenerate case, both with and without coupling. We also derive an upper bound for the efficiency of the cycle. This bound is the same as derived for a system of coupled spin-1/2 particles [G. Thomas and R. S. Johal, Phys. Rev. E 83, 031135 (2011)PLEEE81539-375510.1103/PhysRevE.83.031135], i.e., without degeneracy, and depends only on the control parameters of the Hamiltonian, being independent of the level degeneracy and the reservoir temperatures.

Structure of the thermodynamic arrow of time in classical and quantum theories

In this work we analyse the structure of the thermodynamic arrow of time, defined by transformations that leave the thermal equilibrium state unchanged, in classical (incoherent) and quantum (coherent) regimes. We note that in the infinite-temperature limit the thermodynamic ordering of states in both regimes exhibits a lattice structure. This means that when energy does not matter and the only thermodynamic resource is given by information, the thermodynamic arrow of time has a very specific structure. Namely, for any two states at present there exists a unique state in the past consistent with them and with all possible joint pasts. Similarly, there also exists a unique state in the future consistent with those states and with all possible joint futures. We also show that the lattice structure in the classical regime is broken at finite temperatures, i.e., when energy is a relevant thermodynamic resource. Surprisingly, however, we prove that in the simplest quantum scenario of a two-dimensional system, this structure is preserved at finite temperatures. We provide the physical interpretation of these results by introducing and analysing the history erasure process, and point out that quantum coherence may be a necessary resource for the existence of an optimal erasure process.

Linear irreversible thermodynamics and Onsager reciprocity for information-driven engines.

In the recent progress in nonequilibrium thermodynamics, information has been recognized as a kind of thermodynamic resource that can drive thermodynamic current without any direct energy injection. In this paper, we establish the framework of linear irreversible thermodynamics for a broad class of autonomous information processing. In particular, we prove that the Onsager reciprocity holds true with information: The linear response matrix is well-defined and is shown symmetric with both of the information affinity and the conventional thermodynamic affinity. As an application, we derive a universal bound for the efficiency at maximum power for information-driven engines in the linear regime. Our result reveals the fundamental role of information flow in linear irreversible thermodynamics.

Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamical resource.

Multilevel autonomous quantum thermal machines are discussed. In particular, we explore the relationship between the size of the machine (captured by Hilbert space dimension) and the performance of the machine. Using the concepts of virtual qubits and virtual temperatures, we show that higher dimensional machines can outperform smaller ones. For instance, by considering refrigerators with more levels, lower temperatures can be achieved, as well as higher power. We discuss the optimal design for refrigerators of a given dimension. As a consequence we obtain a statement of the third law in terms of Hilbert space dimension: Reaching absolute zero temperature requires infinite dimension. These results demonstrate that Hilbert space dimension should be considered a thermodynamic resource.

Energy cost of creating quantum coherence

We consider the physical situations where the resource theories of coherence and thermodynamics play competing roles. In particular, we study the creation of quantum coherence using unitary operations with limited thermodynamic resources. We first find the maximal coherence that can be created under unitary operations starting from a thermal state and find explicitly the unitary transformation that creates the maximal coherence. Since coherence is created by unitary operations starting from a thermal state, it requires some amount of energy. This motivates us to explore the trade-off between the amount of coherence that can be created and the energy cost of the unitary process. We find the maximal achievable coherence under the constraint on the available energy. Additionally, we compare the maximal coherence and the maximal total correlation that can be created under unitary transformations with the same available energy at our disposal. We find that when maximal coherence is created with limited energy, the total correlation created in the process is upper bounded by the maximal coherence and vice versa. For two qubit systems we show that there does not exist any unitary transformation that creates maximal coherence and maximal total correlation simultaneously with a limited energy cost.

Thermal-to-electrical energy conversion by diodes under negative illumination

We consider an infrared photodiode under negative illumination, wherein the photodiode is maintained at a temperature $T$ and radiatively exposed to an emissive body colder than itself. We experimentally demonstrate that a diode under such conditions can generate electrical power. We show theoretically that the efficiency of energy conversion can approach the Carnot limit. This work is applicable to waste heat recovery as well as emerging efforts to utilize the cold dark universe as a thermodynamic resource for renewable energy.

Coherence and measurement in quantum thermodynamics.

Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines to solar cells. With thermodynamics predating quantum theory, research now aims to uncover the thermodynamic laws that govern finite size systems which may in addition host quantum effects. Recent theoretical breakthroughs include the characterisation of the efficiency of quantum thermal engines, the extension of classical non-equilibrium fluctuation theorems to the quantum regime and a new thermodynamic resource theory has led to the discovery of a set of second laws for finite size systems. These results have substantially advanced our understanding of nanoscale thermodynamics, however putting a finger on what is genuinely quantum in quantum thermodynamics has remained a challenge. Here we identify information processing tasks, the so-called projections, that can only be formulated within the framework of quantum mechanics. We show that the physical realisation of such projections can come with a non-trivial thermodynamic work only for quantum states with coherences. This contrasts with information erasure, first investigated by Landauer, for which a thermodynamic work cost applies for classical and quantum erasure alike. Repercussions on quantum work fluctuation relations and thermodynamic single-shot approaches are also discussed.

Beyond heat baths: Generalized resource theories for small-scale thermodynamics.

Thermodynamics has recently been extended to small scales with resource theories that model heat exchanges. Real physical systems exchange diverse quantities: heat, particles, angular momentum, etc. We generalize thermodynamic resource theories to exchanges of observables other than heat, to baths other than heat baths, and to free energies other than the Helmholtz free energy. These generalizations are illustrated with "grand-potential" theories that model movements of heat and particles. Free operations include unitaries that conserve energy and particle number. From this conservation law and from resource-theory principles, the grand-canonical form of the free states is derived. States are shown to form a quasiorder characterized by free operations, d majorization, the hypothesis-testing entropy, and rescaled Lorenz curves. We calculate the work distillable from-and we bound the work cost of creating-a state. These work quantities can differ but converge to the grand potential in the thermodynamic limit. Extending thermodynamic resource theories beyond heat baths, we open diverse realistic systems to modeling with one-shot statistical mechanics. Prospective applications such as electrochemical batteries are hoped to bridge one-shot theory to experiments.

Performance limits of multilevel and multipartite quantum heat machines.

We present the general theory of a quantum heat machine based on an N-level system (working medium) whose N-1 excited levels are degenerate, a prerequisite for steady-state interlevel coherence. Our goal is to find out the extent to which coherence in the working medium is an asset for heat machines. The performance bounds of such a machine are common to (reciprocating) cycles that consist of consecutive strokes and continuous cycles wherein the periodically driven system is constantly coupled to cold and hot heat baths. Intriguingly, we find that the machine's performance strongly depends on the relative orientations of the transition-dipole vectors in the system. Perfectly aligned (parallel) transition dipoles allow for steady-state coherence effects, but also give rise to dark states, which hinder steady-state thermalization and thus reduce the machine's performance. Similar thermodynamic properties hold for N two-level atoms conforming to the Dicke model. We conclude that level degeneracy, but not necessarily coherence, is a thermodynamic resource, equally enhancing the heat currents and the power output of the heat machine. By contrast, the efficiency remains unaltered by this degeneracy and adheres to the Carnot bound.

Power enhancement of heat engines via correlated thermalization in a three-level "working fluid".

We explore means of maximizing the power output of a heat engine based on a periodically-driven quantum system that is constantly coupled to hot and cold baths. It is shown that the maximal power output of such a heat engine whose “working fluid” is a degenerate V-type three-level system is that generated by two independent two-level systems. Hence, level degeneracy is a thermodynamic resource that may effectively double the power output. The efficiency, however, is not affected. We find that coherence is not an essential asset in such multilevel-based heat engines. The existence of two thermalization pathways sharing a common ground state suffices for power enhancement.

Radiative cooling of solar absorbers using a visibly transparent photonic crystal thermal blackbody.

A solar absorber, under the sun, is heated up by sunlight. In many applications, including solar cells and outdoor structures, the absorption of sunlight is intrinsic for either operational or aesthetic considerations, but the resulting heating is undesirable. Because a solar absorber by necessity faces the sky, it also naturally has radiative access to the coldness of the universe. Therefore, in these applications it would be very attractive to directly use the sky as a heat sink while preserving solar absorption properties. Here we experimentally demonstrate a visibly transparent thermal blackbody, based on a silica photonic crystal. When placed on a silicon absorber under sunlight, such a blackbody preserves or even slightly enhances sunlight absorption, but reduces the temperature of the underlying silicon absorber by as much as 13 °C due to radiative cooling. Our work shows that the concept of radiative cooling can be used in combination with the utilization of sunlight, enabling new technological capabilities.

Passive radiative cooling below ambient air temperature under direct sunlight.

Cooling is a significant end-use of energy globally and a major driver of peak electricity demand. Air conditioning, for example, accounts for nearly fifteen per cent of the primary energy used by buildings in the United States. A passive cooling strategy that cools without any electricity input could therefore have a significant impact on global energy consumption. To achieve cooling one needs to be able to reach and maintain a temperature below that of the ambient air. At night, passive cooling below ambient air temperature has been demonstrated using a technique known as radiative cooling, in which a device exposed to the sky is used to radiate heat to outer space through a transparency window in the atmosphere between 8 and 13micrometres. Peak cooling demand, however, occurs during the daytime. Daytime radiative cooling to a temperature below ambient of a surface under direct sunlight has not been achieved because sky access during the day results in heating of the radiative cooler by the Sun. Here, we experimentally demonstrate radiative cooling to nearly 5degrees Celsius below the ambient air temperature under direct sunlight. Using a thermal photonic approach, we introduce an integrated photonic solar reflector and thermal emitter consisting of seven layers of HfO2 and SiO2 that reflects 97 per cent of incident sunlight while emitting strongly and selectively in the atmospheric transparency window. When exposed to direct sunlight exceeding 850 watts per square metre on a rooftop, the photonic radiative cooler cools to 4.9degrees Celsius below ambient air temperature, and has a cooling power of 40.1 watts per square metre at ambient air temperature. These results demonstrate that a tailored, photonic approach can fundamentally enable new technological possibilities for energy efficiency. Further, the cold darkness of the Universe can be used as a renewable thermodynamic resource, even during the hottest hours of the day.

Heat-machine control by quantum-state preparation: from quantum engines to refrigerators.

We explore the dependence of the performance bounds of heat engines and refrigerators on the initial quantum state and the subsequent evolution of their piston, modeled by a quantized harmonic oscillator. Our goal is to provide a fully quantized treatment of self-contained (autonomous) heat machines, as opposed to their prevailing semiclassical description that consists of a quantum system alternately coupled to a hot or a cold heat bath and parametrically driven by a classical time-dependent piston or field. Here, by contrast, there is no external time-dependent driving. Instead, the evolution is caused by the stationary simultaneous interaction of two heat baths (having distinct spectra and temperatures) with a single two-level system that is in turn coupled to the quantum piston. The fully quantized treatment we put forward allows us to investigate work extraction and refrigeration by the tools of quantum-optical amplifier and dissipation theory, particularly, by the analysis of amplified or dissipated phase-plane quasiprobability distributions. Our main insight is that quantum states may be thermodynamic resources and can provide a powerful handle, or control, on the efficiency of the heat machine. In particular, a piston initialized in a coherent state can cause the engine to produce work at an efficiency above the Carnot bound in the linear amplification regime. In the refrigeration regime, the coefficient of performance can transgress the Carnot bound if the piston is initialized in a Fock state. The piston may be realized by a vibrational mode, as in nanomechanical setups, or an electromagnetic field mode, as in cavity-based scenarios.

Thermodynamic resource indicators in LCA: a case study on the titania produced in Panzhihua city, southwest China

Purpose While life cycle assessment (LCA) has standardized methods for assessing emission impacts, some comparable methods for the accounting or impact assessment of resource use exist, but are not as mature or standardized. This study contributes to the existing research by offering a comprehensive comparison of the similarities and differences of different resource indicators, in particular those based on thermodynamics, and testing them in a case study on titania (titanium dioxide pigment) produced in Panzhihua city, southwest China.

A systematic methodology for the evaluation of alternative thermochemical cycles for hydrogen production

Abstract Here we present and demonstrate a process systems engineering-based methodology for the initial evaluation of thermochemical cycles for hydrogen production. The five major components of the proposed strategy are (i) conceptualization, (ii) reaction cluster synthesis, (iii) flowsheet design, simulation, and analysis, (iv) process integration and (v) performance evaluation. The resulting approach involves selecting atomic and molecular species with desired properties, identifying suitable thermodynamically feasible cycles of reactions based on these species, screening and sequencing the most promising of the identified reaction clusters, designing a process of unit operations to carry out the reaction cluster, and integrating those processes to maximize thermodynamic efficiency and resource utilization. An integrated suite of resources, including AspenOne software, is employed to aid in implementation of the algorithm. The strength of the proposed methodology is demonstrated through an illustrative example involving the commonly studied Fe–Cl system. The results of our systematic evaluation provide cycles with estimated base efficiencies ranging from 35% to 49%.

Efficient implementation and the product-state representation of numbers

The relation between the requirement of efficient implementability and the product-state representation of numbers is examined. Numbers are defined to be any model of the axioms of number theory or arithmetic. Efficient implementability (EI) means that the basic arithmetic operations are physically implementable and the space-time and thermodynamic resources needed to carry out the implementations are polynomial in the range of numbers considered. Different models of numbers are described to show the independence of both EI and the product-state representation from the axioms. The relation between EI and the product-state representation is examined. It is seen that the condition of a product-state representation does not imply EI. Arguments used to refute the converse implication, EI implies a product-state representation, seem reasonable; but they are not conclusive. Thus this implication remains an open question.

Representation of natural numbers in quantum mechanics

This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural numbers or a model of arithmetic if the set and operations satisfy the axioms of number theory or arithmetic. This paper is limited to $k\ensuremath{-}\mathrm{ary}$ representations of length L and to the axioms for arithmetic modulo ${k}^{L}.$ A model of the axioms is described based on an abstract L-fold tensor product Hilbert space ${\mathcal{H}}^{\mathrm{arith}}.$ Unitary maps of this space onto a physical parameter based product space ${\mathcal{H}}^{\mathrm{phy}}$ are then described. Each of these maps makes states in ${\mathcal{H}}^{\mathrm{phy}},$ and the induced operators, a model of the axioms. Consequences of the existence of many of these maps are discussed along with the dependence of Grover's and Shor's algorithms on these maps. The importance of the main physical requirement, that the basic arithmetic operations are efficiently implementable, is discussed. This condition states that there exist physically realizable Hamiltonians that can implement the basic arithmetic operations and that the space-time and thermodynamic resources required are polynomial in L.