Zeroth Law Of Thermodynamics Research Articles

Approach to Equilibrium in Translation-Invariant Quantum Systems: Some Structural Results

We formulate the problem of approach to equilibrium in algebraic quantum statistical mechanics and study some of its structural aspects, focusing on the relation between the zeroth law of thermodynamics (approach to equilibrium) and the second law (increase in entropy). Our main result is that approach to equilibrium is necessarily accompanied by a strict increase in the specific (mean) energy and entropy. In the course of our analysis, we introduce the concept of quantum weak Gibbs state which is of independent interest.

Kinetic Temperature of Structures for Resilience, Instability, and Failure Analysis of Building Systems

From theory, calibration and application of the equipartition theorem of statistical physics to structural failure and instability analysis, we introduce the kinetic temperature of structures as an order parameter to ascertain equilibrium and out-of-equilibrium states in structural mechanics. Set within the framework of molecular dynamics-based structural mechanics, this is achieved by connecting the set of momentum balance equations to an outside bath reservoir maintained at a reference temperature history through the Nosé-Hoover thermostat. The problem thus comes down to solving the momentum balance equation with a dissipative mass damping term, which evolves in function of the difference in temperature between the structure’s kinetic temperature/energy and the bath temperature. Following the Zeroth Law of Thermodynamics, it is recognized that a structure is in (thermal) equilibrium as long as the structure’s kinetic temperature attains the bath temperature; whereas it is out-of-equilibrium when the open system (structure plus bath) exhibits a sustained temperature difference. In this case, the structure has exhausted its fluctuation-dissipation capacity, which is indicative—for structures—of a progressive failure and instability. The implementation of the kinetic temperature as an order parameter in structural failure and instability analysis is illustrated for a prototype five-storey building subject to excessive wind and fire loads. It is suggested that the proposed order parameter becomes an integral part of the structural engineering toolbox for resilience studies of buildings and structures.

Operational Definition of the Temperature of a Quantum State.

Temperature is usually defined for physical systems at thermal equilibrium. Nevertheless one may wonder if it would be possible to attribute a meaningful notion of temperature to an arbitrary quantum state, beyond simply the thermal (Gibbs) state. In this Letter, we propose such a notion of temperature considering an operational task, inspired by the zeroth law of thermodynamics. Specifically, we define two effective temperatures for quantifying the ability of a quantum system to cool down or heat up a thermal environment. In this way we can associate an operationally meaningful notion of temperature to any quantum density matrix. We provide general expressions for these effective temperatures, for both single- and many-copy systems, establishing connections to concepts previously discussed in the literature. Finally, we consider a more sophisticated scenario where the heat exchange between the system and the thermal environment is assisted by a quantum reference frame. This leads to an effect of "coherent quantum catalysis," where the use of a coherent catalyst allows for exploiting quantum energetic coherences in the system, now leading to much colder or hotter effective temperatures. We demonstrate our findings using a two-level atom coupled to a single mode of the electromagnetic field.

Modernizing Furnace Systems at Oil Refineries for Multifunctionality

At oil refineries, furnaces account for much of the energy expenditure. Energy efficiency may be improved by means of an integrated system that contains a furnace and a unit for heating the incoming gas with energy recovered from the smokestack gases. By exergetic analysis and efficiency assessment of the energy distribution in the system (on the basis of the zeroth law of thermodynamics), a multifunctional approach to effective integration of the furnace subsystem and the energy subsystem is proposed. That results in greater stability of the integrated system; provides the energy required for all the technological operations, as well as additional inexpensive electrical power; and helps curb thermal pollution of the environment. This approach may be adopted in modernizing existing systems or creating new systems.

The Zeroth Law of Thermodynamics in Special Relativity

We critically revisit the definition of thermal equilibrium, in its operational formulation, provided by standard thermodynamics. We show that it refers to experimental conditions which break the covariance of the theory at a fundamental level and that, therefore, it cannot be applied to the case of moving bodies. We propose an extension of this definition which is manifestly covariant and can be applied to the study of isolated systems in special relativity. The zeroth law of thermodynamics is, then, proven to establish an equivalence relation among bodies which have not only the same temperature, but also the same center of mass four-velocity.

Thermodynamic Foundations of an Information-Based Systems Approach to Designing Complex Engineering Objects

Thermodynamic foundations of an information-based systems approach to designing complex engineering objects with hierarchical structure using macrolevel and microlevel models are presented in application to chemical engineering systems. The hierarchical structure of a chemical engineering system is characterized by three levels: the system as a whole, chemical-engineering processes (elements of the system), and microstates (results of transformations). The design of the elements of the system is based on the thermodynamic model at the microlevel. After a certain formalization of matter and energy transformations, this model characterizes the process of information acquisition. The design of the chemical engineering system on the macrolevel is described by a model of a stochastic process of the fluctuation of average process energy levels. This model establishes the coordinated operation of the elements of the system according to the zeroth law of thermodynamics. A minimax problem of the optimal design of a complex engineering object is formulated. The problem is based on a combination of three laws of thermodynamics: the first, the second, and the zeroth, which allows one to achieve emergent properties of the system as a whole.

Zeroth laws– hiding in plain sight [Basicmetrology

The most famous and widely accepted is the zeroth law of thermodynamics. The first and second laws were already in place, but a preliminary law was seen to be missing, perhaps because it was too obvious. The missing piece postulates the existence of temperature and provides the rationale behind instruments (thermometers) that can measure temperature. It is this metrological oversight that makes this zeroth law and others like it a fit subject for a column on basic metrology.

Šesták’s proposal of term “tempericity” for non-equilibrium temperature and modified Tykodi’s thermal science classification with regard to methods of thermal analysis

The equilibrium (thermodynamic) temperature of a body is defined by zeroth law of thermodynamics as a quantity obtained by thermometer as a result of thermal equilibrium between the body and the thermometer. However, the term temperature is also used for description of any instantaneous thermal state during processes where no thermal equilibrium is reached. The proposal of Tykodi to divide thermal science into three branches has been modified to express the dependence of temperature on time and position inside a system. The three branches have been called thermostatics (equilibrium thermodynamics), thermostatics (thermodynamics of steady = stationary states) and thermokinetics (thermal science dealing with unsteady—non-stationary states). Equilibrium temperature is used only at thermostatics. For other branches of thermal science where the Newton cooling law and/or any of both Fourier laws are applied, no equilibrium temperature with respect to zeroth law is expected. Thermal analysis studying unsteady states (temperature is a function of time t as well as of space coordinates x) should be subject of thermokinetics, and the appropriate kinetic models should include the local temperature changes evoked by self-cooling or self-heating due to process running inside sample.

Exergization

Exergization

Zeroth law and nonequilibrium thermodynamics for steady states in contact.

We ask what happens when two nonequilibrium systems in steady state are kept in contact and allowed to exchange a quantity, say mass, which is conserved in the combined system. Will the systems eventually evolve to a new stationary state where a certain intensive thermodynamic variable, like equilibrium chemical potential, equalizes following the zeroth law of thermodynamics and, if so, under what conditions is it possible? We argue that an equilibriumlike thermodynamic structure can be extended to nonequilibrium steady states having short-ranged spatial correlations, provided that the systems interact weakly to exchange mass with rates satisfying a balance condition-reminiscent of a detailed balance condition in equilibrium. The short-ranged correlations would lead to subsystem factorization on a coarse-grained level and the balance condition ensures both equalization of an intensive thermodynamic variable as well as ensemble equivalence, which are crucial for construction of a well-defined nonequilibrium thermodynamics. This proposition is proved and demonstrated in various conserved-mass transport processes having nonzero spatial correlations.

Deterministic time-reversible thermostats: chaos, ergodicity, and the zeroth law of thermodynamics

The relative stability and ergodicity of deterministic time-reversible thermostats, both singly and in coupled pairs, are assessed through their Lyapunov spectra. Five types of thermostat are coupled to one another through a single Hooke’s-law harmonic spring. The resulting dynamics shows that three specific thermostat types, Hoover–Holian, Ju–Bulgac, and Martyna–Klein–Tuckerman, have very similar Lyapunov spectra in their equilibrium four-dimensional phase spaces and when coupled in equilibrium or nonequilibrium pairs. All three of these oscillator-based thermostats are shown to be ergodic, with smooth analytic Gaussian distributions in their extended phase spaces (coordinate, momentum, and two control variables). Evidently these three ergodic and time-reversible thermostat types are particularly useful as statistical-mechanical thermometers and thermostats. Each of them generates Gibbs’ universal canonical distribution internally as well as for systems to which they are coupled. Thus they obey the zeroth law of thermodynamics, as a good heat bath should. They also provide dissipative heat flow with relatively small nonlinearity when two or more such temperature baths interact and provide useful deterministic replacements for the stochastic Langevin equation.

Local temperature of out-of-equilibrium quantum electron systems

We show how the local temperature of out-of-equilibrium, quantum electron systems can be consistently defined with the help of an external voltage and temperature probe. We determine sufficient conditions under which the temperature measured by the probe (i) is independent of details of the system-probe coupling, (ii) is equal to the temperature obtained from an independent current-noise measurement, (iii) satisfies the transitivity condition expressed by the zeroth law of thermodynamics, and (iv) is consistent with Carnot's theorem. This local temperature therefore characterizes the system in the common sense of equilibrium thermodynamics, but remains well defined even in out-of-equilibrium situations with no local equilibrium.

Dynamical consequences of a constraint on the Langevin thermostat in molecular cluster simulation

We investigate some unusual behaviour observed while performing molecular dynamics simulations of small molecular clusters using a constrained Langevin thermostat. Atoms appear to be thermalised to different temperatures that depend on their mass and on the total number of particles in the system. The deviation from the zeroth law of thermodynamics can be considerable for small systems of heavy and light particles. We trace this behaviour to the absence of thermal noise acting on the centre of mass of the system. This is demonstrated by solving the stochastic dynamics for the constrained thermostat and comparing the results with simulation data. By removing the constraint, the Langevin thermostat may be restored to its intended behaviour. We also investigate a Langevin thermostat constrained to have zero total force acting on its centre of mass, and find similar deficiencies.

Brownian localization: A generalized coupling model yielding a nonergodic Langevin equation description

A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed, which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling. This model allows ballistic diffusion and classical localization simultaneously, in which the fluctuation-dissipation relation is still satisfied but the Khinchin theorem is broken. The asymptotical equilibrium for a nonergodic system requires the initial thermal equilibrium, however, when the system starts from nonthermal conditions, it does not approach the equilibration even though a nonlinear potential is used to bound the particle, this can be confirmed by the zeroth law of thermodynamics. In the dynamics of Brownian localization, due to the memory damping function inducing a constant term, our results show that the stationary distribution of the system depends on its initial preparation of coordinate rather than momentum. The coupled oscillator chain with a fixed end boundary acts as a heat bath, which has long been used in studies of collinear atom/solid-surface scattering and lattice vibration, we investigate this problem from the viewpoint of nonergodicity.

Zeroth law compatibility of nonadditive thermodynamics

Nonextensive thermodynamics is criticized by the statement that the zeroth law cannot be satisfied with nonadditive composition rules [corrected]. In this paper we determine the general functional form of those nonadditive composition rules that are compatible with the zeroth law of thermodynamics. We find that this general form is additive for the formal logarithms of the original quantities and the familiar relations of thermodynamics apply to these. Our result offers a possible solution to the long-standing questions about equilibrium between extensive and nonextensive systems or systems with different nonextensivity parameters.

Statistical thermodynamics of moving bodies

We resolve the long standing question of temperature dependence of uniformly moving bodies by means of a quantum statistical treatment centred on the zeroth law of thermodynamics. The key to our treatment is the result, established by Kossakowski et al, that a macroscopic body behaves as a thermal reservoir with well-defined temperature, in the sense of the zeroth law, if and only if its state satisfies the Kubo-Martin-Schwinger (KMS) condition. In order to relate this result to the relativistic thermodynamics of moving bodies, we employ the Tomita-Takesaki modular theory to prove that a state cannot satisfy the KMS conditions with respect to two different inertial frames whose relative velocity is non-zero. This implies that the concept of temperature stemming from the zeroth law is restricted to states of bodies in their rest frames and thus that there is no law of temperature transformations under Lorentz boosts. The corresponding results for nonrelativistic Galilean systems have also been established.

Comment on “Violation of the Zeroth Law of Thermodynamics in Systems with Negative Specific Heat”

A Comment on the Letter by A. Ram\'{\i}rez-Hern\'andez, H. Larralde, and F. Leyvraz, Phys. Rev. Lett. 100, 120601 (2008). The authors of the Letter offer a Reply.

Two long-standing problems in Tsallis’ statistics

On the basis of Tsallis’ entropy and the joint probability factorization condition, two controversial problems existing in Tsallis’ statistics are investigated, where one is whether energy is extensive or not and the other is whether it is necessary to introduce the so-called generalized zeroth law of thermodynamics or not. The results obtained show clearly that like entropy, energy is also nonextensive in Tsallis’ statistics, and that the zeroth law of thermodynamics has been implicitly used in Tsallis’ statistics since 1988. Moreover, it is expounded that the standard energy additivity rule adopted by a great number of researchers is not suitable in Tsallis’ statistics, because its corollary is in contradiction with the zeroth law of thermodynamics.

Two long-standing problems in Tsallis’ statistics

On the basis of Tsallis’ entropy and the joint probability factorization condition, two controversial problems existing in Tsallis’ statistics are investigated, where one is whether energy is extensive or not and the other is whether it is necessary to introduce the so-called generalized zeroth law of thermodynamics or not. The results obtained show clearly that like entropy, energy is also nonextensive in Tsallis’ statistics, and that the zeroth law of thermodynamics has been implicitly used in Tsallis’ statistics since 1988. Moreover, it is expounded that the standard energy additivity rule adopted by a great number of researchers is not suitable in Tsallis’ statistics, because its corollary is in contradiction with the zeroth law of thermodynamics.

Stochastic invertible mappings for Tsallis distributions

We devise mappings between Gaussian distributions and power-law distributions, nowadays also called Tsallis distributions. To a given Tsallis distributed vector X, one can associate a Gaussian distributed vector N in the fashion N = a X where a is a random variable independent of X whose properties we are going to characterize here. We not only show that this mapping is invertible but also construct the adequate inversion operation. As an application of this stochastic mapping, we revisit the problem posed to Tsallis practitioners by the zeroth law of thermodynamics, that has bedeviled them for 15 years. To cite this article: C. Vignat, A. Plastino, C. R. Physique 7 (2006).