Quantum Fluctuation Theorem for Arbitrary Measurement and Feedback Schemes.

<p indent=0mm>Maxwell’s demon challenged the second law of thermodynamics, thereby attracting much research attention for over a century. As this system does not exchange energy with circumstances, the energy is conserved. Consequently, it is useless to analyze this problem from an energy viewpoint. Therefore, numerous studies have been conducted to analyze the entropy change in this process. Further, a conclusion was reached that the irreversibility process of obtaining information necessarily induces the entropy production, so the whole system still satisfies the entropy increase principle in an isolated system. This study demonstrates that Maxwell’s demon still follows the second law of thermodynamics from an energy conservation viewpoint in a macroscopic reversible process. Thermomass theory recognizes the mass nature of heat in the transfer process and proposes a new quantity called thermomass, which is the extra mass due to thermal vibration. Additionally, thermomass energy is a kind of relativistic energy that is carried by thermomass, and it is far smaller than that carried by the rest of the mass. To move the same amount of heat from a lower to a higher temperature region, the reversible thermodynamics analyses show that what is supposed to be input into the system can be thermomass energy and not necessarily external work or heat (conventional energy). Moreover, the negative entropy carried by heat corresponds to the positive thermomass energy and not the product of entropy and temperature. Inspired and motivated by these results, this study reconsiders the revised Maxwell’s demon system following the viewpoint of thermomass energy and relativistic energy and explains their influences on the system from the introduction of information. There are two Maxwell’s demons and two gates, and the chosen molecules can pass the gates one by one. Furthermore, when there is a molecule passing through gate 1 from left to right, another molecule concurrently passes through gate 2 from right to left with a different speed. Thus, the numbers of molecules at both sides remain unchanged. Thus, these two parts have constant density and heat capacity, thereby making quantitative and qualitative analyses easier. Moreover, the whole system is in equilibrium state at the beginning. Then, Maxwell’s demons exchange the thermal energy and temperature difference arises between these two sides. The entropy in the gas system decreases, whereas the thermomass energy increases. No work or heat is input into this system, while the same amount of heat is carried from the low-temperature region to the high-temperature one. If the exchange process is slow enough, this process can be considered as a reversible one. Thus, the entropy and thermomass energy are supposed to be conserved, implying that the information obtained by the demons during the operation concurrently carries the negative entropy and positive thermomass energy. Furthermore, the energy carried by the information is called information energy, which is also a kind of relativistic energy. Therefore, it is the information energy that has been reversibly input into the system to promote heat transfer and not the external work or heat. In this way, the reversible energy conservation analyses demonstrate that Maxwell’s demon problem still follows the second law of thermodynamics. Moreover, this process reveals that the negative entropy carried by the information corresponds to the positive thermomass energy and not the product of entropy and temperature.

Investigation of thermal characteristics and entropy generation in a solar collector including Fly Ash-Cu hybrid nanofluids: Numerical approach using mixture model

In this work, we have considered a non-canonical scalar field dark energy model in the framework of flat FRW background. It has also been assumed that the dark matter sector interacts with the non-canonical dark energy sector through some interaction term. Using the solutions for this interacting non-canonical scalar field dark energy model, we have investigated the validity of generalized second law (GSL) of thermodynamics in various scenarios using first law and area law of thermodynamics. For this purpose, we have assumed two types of horizons viz apparent horizon and event horizon for the universe and using first law of thermodynamics, we have examined the validity of GSL on both apparent and event horizons. Next, we have considered two types of entropy-corrections on apparent and event horizons. Using the modified area law, we have examined the validity of GSL of thermodynamics on apparent and event horizons under some restrictions of model parameters.

The fluctuation theorem is the fundamental equality in nonequilibrium thermodynamics that is used to derive many important thermodynamic relations, such as the second law of thermodynamics and the Jarzynski equality. Recently, the thermodynamic uncertainty relation was discovered, which states that the fluctuation of observables is lower bounded by the entropy production. In the present Letter, we derive a thermodynamic uncertainty relation from the fluctuation theorem. We refer to the obtained relation as the fluctuation theorem uncertainty relation, and it is valid for arbitrary dynamics, stochastic as well as deterministic, and for arbitrary antisymmetric observables for which a fluctuation theorem holds. We apply the fluctuation theorem uncertainty relation to an overdamped Langevin dynamics for an antisymmetric observable. We demonstrate that the antisymmetric observable satisfies the fluctuation theorem uncertainty relation but does not satisfy the relation reported for current-type observables in continuous-time Markov chains. Moreover, we show that the fluctuation theorem uncertainty relation can handle systems controlled by time-symmetric external protocols, in which the lower bound is given by the work exerted on the systems.

There are two primary laws including the first and second laws of thermodynamics that should be used to assess a process. Generally, only the first law of thermodynamics is investigated in numerical solutions, so it is possible to exist some numerical results that do not satisfy the second law of thermodynamics because of numerical errors. To achieve reliable numerical outcomes, it is better to apply two indexes of HEAT BALANCE ERROR and VIRTUAL ENTROPY GENERATION, which come from the second law of thermodynamics. In other words, an approach to develop computational fluid dynamics investigations is to take second law of thermodynamics into consideration. In this study, two different models including counterflow double‐pipe heat exchanger and single‐pipe with constant wall temperature are simulated in various cases with different efficiencies and temperature ratios. It is found that 46 cases of total 523 double‐pipe models and 24 cases of total 402 simulations of single‐pipe models had unacceptable results regarding to two mentioned criteria. The results revealed that it is less likely to gain unreliable results in smaller efficiency and lower inlet temperature for double‐pipe heat exchanger and single‐pipe respectively.

A stopping time T is the first time when a trajectory of a stochastic process satisfies a specific criterion. In this paper, we use martingale theory to derive the integral fluctuation relation for the stochastic entropy production in a stationary physical system at stochastic stopping times T. This fluctuation relation implies the law , which states that it is not possible to reduce entropy on average, even by stopping a stochastic process at a stopping time, and which we call the second law of thermodynamics at stopping times. This law bounds the average amount of heat and work a system can extract from its environment when stopped at a random time. Furthermore, the integral fluctuation relation implies that certain fluctuations of entropy production are universal or are bounded by universal functions. These universal properties descend from the integral fluctuation relation by selecting appropriate stopping times: for example, when T is a first-passage time for entropy production, then we obtain a bound on the statistics of negative records of entropy production. We illustrate these results on simple models of nonequilibrium systems described by Langevin equations and reveal two interesting phenomena. First, we demonstrate that isothermal mesoscopic systems can extract on average heat from their environment when stopped at a cleverly chosen moment and that the second law at stopping times bounds the average extracted heat. Second, we demonstrate that the efficiency at stopping times of an autonomous stochastic heat engine, such as Feymann’s ratchet, can be larger than the Carnot efficiency and that the second law of thermodynamics at stopping times bounds its efficiency at stopping times.

In the work reported in this paper, we have analyzed generalized Chaplygin gas (GCG) and modified generalized Chaplygin gas (MGCG) in an interacting scenario. The equation of state parameter has been analyzed in both the cases and the stability of the models has been discerned through squared speed of sound. Stability against gravitational perturbations has been observed for both GCG and MGCG interacting with pressureless dark matter. Also, the generalized second law (GSL) of thermodynamics has been tested for different enveloping horizons and validity of GSL has been observed throughout. Furthermore, f(T) gravity has been reconstructed with GCG and MGCG and phantom behaviour has been observed through reconstructed EoS parameters. The squared speed of sound has been derived for f(T) gravity and stability of the model has been established through its positivity.

We provide a short review of the recent developments in entropic cosmology based on two thermodynamic laws of the apparent horizon, namely the first and the second laws of thermodynamics. The first law essentially provides the change in entropy of the apparent horizon during the cosmic evolution of the universe; in particular, it is expressed by TdS=−d(ρV)+WdV (where W is the work density and other quantities have their usual meanings). In this way, the first law actually links various theories of gravity with the entropy of the apparent horizon. This leads to a natural question—“What is the form of the horizon entropy corresponding to a general modified theory of gravity?”. The second law of horizon thermodynamics states that the change in total entropy (the sum of horizon entropy + matter fields’ entropy) with respect to cosmic time must be positive, where the matter fields behave like an open system characterised by a non-zero chemical potential. The second law of horizon thermodynamics importantly provides model-independent constraints on entropic parameters. Finally, we discuss the standpoint of entropic cosmology on inflation (or bounce), reheating and primordial gravitational waves from the perspective of a generalised entropy function.

We introduce a class of random mechanical systems called random billiards to study the problem of quantifying the irreversibility of nonequilibrium macroscopic systems. In a random billiard model, a point particle evolves by free motion through the interior of a spatial domain, and reflects according to a reflection operator, specified in the model by a Markov transition kernel, upon collision with the boundary of the domain. We derive a formula for entropy production rate that applies to a general class of random billiard systems. This formula establishes a relation between the purely mathematical concept of entropy production rate and textbook thermodynamic entropy, recovering in particular Clausius' formulation of the second law of thermodynamics. We also study an explicit class of examples whose reflection operator, referred to as the Maxwell-Smolukowski thermostat, models systems with boundary thermostats kept at possibly different temperatures. We prove that, under certain mild regularity conditions, the class of models are uniformly ergodic Markov chains and derive formulas for the stationary distribution and entropy production rate in terms of geometric and thermodynamic parameters.

In this paper, the second law of thermodynamics in the public basic course college physics was taken as an example to achieve the heuristic teaching design with students as the main body. The logical framework of knowledge was reconstructed based on combing knowledge points. This lesson takes the directionality of natural process as the main line, and connects the written expression and mathematical representation of the second law of thermodynamics from macro and micro perspectives, enables students to understand and grasp the essence of the second law of thermodynamics and entropy, and establish the logical connection between the two. At the same time, this lesson integrates current hot topics, organizes ideological and political elements, advances from knowledge to thought layer by layer, and carries out closed-loop teaching that integrates scientific knowledge and humanistic literacy, theoretical learning and practical cognition, achieving the teaching goal of imparting knowledge and educating people, and providing more ideas and references for the teaching design of college physics course under the background of ideological and political education.

The science of thermodynamics is built primarily on two fundamentally natural laws, known as the first and second laws. The first law of thermodynamics is simply an expression of the conservation of energy principle. It asserts that energy is a thermodynamic property, and that during an interaction, energy can change from one form to another but the total amount of energy remains constant. The second law of thermodynamics asserts that energy has quality as well as quantity, and actual processes occur in the direction of decreasing quality of energy. The attempts to quantify the quality or “work potential” of energy in light of the second law of thermodynamics has resulted in the definition of the property named exergy. In this chapter, basic relations for the first and second laws of thermodynamics are provided for closed systems and control volumes. The concepts of entropy and exergy derived from the second law are thoroughly discussed.KeywordsEntropy ChangeEntropy GenerationHeat EngineExergy AnalysisExergy EfficiencyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The second law of thermodynamics has been proven by many facts in classicalworld. Is there any new property of it in quantum world? In this paper, wecalculate the change of entropy in T.D. Kieu's model for quantum heat engine(QHE) and prove the broad validity of the second law of thermodynamics. Itis shown that the entropy of the quantum heat engine neither decreases in awhole cycle, nor decreases in either stage of the cycle. The second law ofthermodynamics still holds in this QHE model. Moreover, although themodified quantum heat engine is capable of extracting more work, itsefficiency does not improve at all. It is neither beyond the efficiencyof T.D. Kieu's initial model, nor greater than the reversible Carnot efficiency.

A generalization of the Onsager-Machlup theory from equilibrium to nonequilibrium steady states and its connection with recent fluctuation theorems are discussed for a dragged particle restricted by a harmonic potential in a heat reservoir. Using a functional integral approach, the probability functional for a path is expressed in terms of a Lagrangian function from which an entropy production rate and dissipation functions are introduced, and nonequilibrium thermodynamic relations like the energy conservation law and the second law of thermodynamics are derived. Using this Lagrangian function we establish two nonequilibrium detailed balance relations, which not only lead to a fluctuation theorem for work but also to one related to energy loss by friction. In addition, we carried out the functional integrals for heat explicitly, leading to the extended fluctuation theorem for heat. We also present a simple argument for this extended fluctuation theorem in the long time limit.

Two fundamental questions are still open about the complex relation between fluid dynamics and thermodynamics. Is it possible (and convenient) to describe fluid dynamic in terms of second law based thermodynamic equations? Is it possible to solve and manage fluid dynamics problems by mean of second law of thermodynamics? This chapter analyses the problem of the relationships between the laws of fluid dynamics and thermodynamics in both first and second law of thermodynamics in the light of constructal law. In particular, taking into account constructal law and the diffusive formulation of Bejan number, it defines a preliminary step through an extensive thermodynamic vision of fluid dynamic phenomena.

Introduction: From the thermodynamic perspective, the diaphragm is an open thermal system and can be regarded as a machine (piston) that converts part of the consumed power in external power during a breathing cycle. Aims and objectives: Aim of the study is to determine the exergy destruction and entropy generation by using thermodynamic analysis of the work done in the diaphragm muscle. Methods: In this study, a human respiratory system was modeled as the diaphragm skeletal muscle. Then, the first and second laws of thermodynamics were utilized to analyze these systems. Mass, energy, exergy and entropy balances are performed around the diaphragm muscles to calculate the glucose consumption, exergy destruction and entropy generation. Results: As a result of the thermodynamic analysis of the work for resting state respiration (diaphragm) performed by a healthy adult individual, the minimum and maximum values of the exergy destruction were calculated to change from 8.41x10-3 kJ/min to 12x10-3 kJ/min, respectively. Entropy generation was found to be between 2.82x10-5 and 4.03x10-5. The glucose used by the diaphragm muscle is calculated for minimum and maximum work values. Given the results of the energy balance analysis according to the first law of thermodynamics, the glucose consumed for this work was calculated as 0.22-0.31 mmol/min. Conclusions: When the muscle work done by the diaphragm is maximized, exergy destruction is also increasing. In individuals with Chronic Obstructive Pulmonary Disease, considering the increased muscle work to be done for respiration, entropy generation may be expected to increase further in these patients.