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Xibei Nong-Lin Keji Daxue xuebao. Ziran kexue ban

The relativity of negative absolute temperature system

Xi Wang

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

The paper draws the concept of negative absoute temperature form thermodynamic system,studies the reationship between energy,absolute temperature and entropy in accordance with operating principle of laser and on the basis of which,the relativity of negative absoleete temperature is discussed.

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A system, or a set of systems, is said to be in thermal equilibrium when no net flow of heat energy occurs between its constituent parts when they are connected by a path permeable to heat (a diathermal wall).1 This condition is the endpoint of a spontaneous process: if two bodies at different temperatures are brought into thermal contact, energy will flow from the higher-temperature object to the lower-temperature object until this flow ceases and the equilibrium state is achieved.3 Within a single system, thermal equilibrium is characterized by a temperature that is both spatially uniform (the same at all points) and temporally constant (unchanging over time).4 This uniformity of macroscopic properties—such as temperature and pressure—is what defines the state of the system.1 It is important to distinguish this from the broader state of thermodynamic equilibrium. Thermal equilibrium (uniform temperature) is a necessary component, but full thermodynamic equilibrium also requires mechanical equilibrium (uniform pressure) and diffusive equilibrium (uniform chemical potential).6 Systems can achieve thermal equilibrium without achieving full thermodynamic equilibrium.6 The Zeroth Law of Thermodynamics: The "Discovery" of Temperature The concept of temperature, while intuitive, requires a formal physical principle to exist as a measurable, fundamental property. This principle is the Zeroth Law of Thermodynamics. Although it was formulated and named after the First and Second Laws, its foundational role was recognized as a logical prerequisite for the entire structure of thermodynamics.8 The law states: If system A is in thermal equilibrium with system C, and system B is in thermal equilibrium with system C, then systems A and B are in thermal equilibrium with each other.1 In this construction, system C plays the role of a thermometer.13 The profound implication of this law is mathematical: it establishes thermal equilibrium as a transitive relation 9, or more formally, an equivalence relation.14 In mathematics, any equivalence relation partitioning a set of objects implies the existence of a common, scalar property shared by all members of a given equivalence class. The Zeroth Law thus proves the existence of a scalar function of state—a property we call temperature—that is common to all systems in mutual thermal equilibrium.9 The law is, therefore, the fundamental basis for defining temperature and building consistent, reproducible temperature scales.1 This axiomatic foundation also provides the logical origin for one of temperature's most critical characteristics: it is an intensive property. An intensive property is one that does not depend on the size or amount of the system.15 If a large system 'A' is in internal thermal equilibrium 6, any two parts of it, subsystems 'A1' and 'A2', must also be in thermal equilibrium with each other. By the Zeroth Law, a thermometer 'C' that is in thermal equilibrium with the whole system 'A' must also be in thermal equilibrium with 'A1' and 'A2' individually.13 The thermometer, therefore, gives the same reading for all three. This demonstrates that the temperature of a system in thermal equilibrium is the same as the temperature of any part of it.16

•Nov 14, 2025•0 citations
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper, I analyze and calculate the thermodynamic entropy for large but finite quantum mechanical systems. A special feature of this analysis is that the thermodynamic energy of a quantum system is shown to be a continuous variable, rather than being associated with discrete energy eigenvalues. Calculations of the entropy as a function of energy can be carried out with a Legendre transform of thermodynamic potentials obtained from a canonical ensemble. The resultant expressions for the entropy are able to describe equilibrium between quantum systems having incommensurate energy-level spacings. This definition of entropy preserves all required thermodynamic properties, including satisfaction of all postulates and laws of thermodynamics. It demonstrates the consistency of the concept of negative temperature with the principles of thermodynamics.
Negative absolute temperature, defined in terms of the Boltzmann factor, corresponds to an upside-down energy pyramid. The example of the laser shows population inversion to be accompanied by the switch from absorption to emission, that is, from positive to negative dissipation, from increasing disorder throughout a system to increasing order in a subsystem. Early treatments of the negative-temperature concept are by Onsager and by Ramsey. Ramsey’s ’’essential requirements’’ are shown to be too strong. A TS diagram for a Carnot cycle operating between two negative temperatures clarifies the origin of amplification. Some biological negative-resistance amplifiers (nerve, muscle), in particular those involving ordered arrays of water molecules, are conjectured to have negative-temperature subsystems.
Small systems consisting of a few particles are increasingly technologically relevant. In such systems, an intense debate in microcanonical statistical mechanics has been about the correctness of Boltzmann's surface entropy versus Gibbs' volume entropy. Both entropies have shortcomings─while Boltzmann entropy predicts unphysical negative/infinite absolute temperatures for small systems with an unbounded energy spectrum, Gibbs entropy entirely disallows negative absolute temperatures, in disagreement with experiments. We consider a relative energy window, motivated by the Heisenberg energy-time uncertainty principle and eigenstate thermalization in quantum mechanics. The proposed entropy ensures positive, finite temperatures for systems without a maximum limit on their energy and allows negative absolute temperatures in bounded energy spectrum systems, e.g., with population inversion. It also closely matches canonical ensemble predictions for prototypical systems, thus correctly describing the zero-point energy of an isolated quantum harmonic oscillator. Overall, we enable accurate thermodynamic models for isolated systems with few degrees of freedom.
According to the famous thinking experiment EPR, in quantum mechanics there exists unfixed range effect. This statement contradicts the theory of relativity, which says the velocity of light is the fastest in nature. The contradiction remains unsettled for so many years. Therefore, the paper presents that there may be some disharmony in the relativistic quantum mechanics and quantum field theory, and there are no solutions to these problems. It is tried to probe into these problems by digging into negative energy. Researches show negative energy not only is a method for mathematical computation, but also has its real physical contents. This paper extends the special theory of relativity to negative energy system, puts forward new ideas, and draws out the new form of time-space transformation, which can theoretically explain the unfixed range effect without destroying the causality. The relevant equation is developed by combining the theory of negative energy system and the theory of quantum mechanics.
A system, or a set of systems, is said to be in thermal equilibrium when no net flow of heat energy occurs between its constituent parts when they are connected by a path permeable to heat (a diathermal wall).1 This condition is the endpoint of a spontaneous process: if two bodies at different temperatures are brought into thermal contact, energy will flow from the higher-temperature object to the lower-temperature object until this flow ceases and the equilibrium state is achieved.3 Within a single system, thermal equilibrium is characterized by a temperature that is both spatially uniform (the same at all points) and temporally constant (unchanging over time).4 This uniformity of macroscopic properties—such as temperature and pressure—is what defines the state of the system.1 It is important to distinguish this from the broader state of thermodynamic equilibrium. Thermal equilibrium (uniform temperature) is a necessary component, but full thermodynamic equilibrium also requires mechanical equilibrium (uniform pressure) and diffusive equilibrium (uniform chemical potential).6 Systems can achieve thermal equilibrium without achieving full thermodynamic equilibrium.6 The Zeroth Law of Thermodynamics: The "Discovery" of Temperature The concept of temperature, while intuitive, requires a formal physical principle to exist as a measurable, fundamental property. This principle is the Zeroth Law of Thermodynamics. Although it was formulated and named after the First and Second Laws, its foundational role was recognized as a logical prerequisite for the entire structure of thermodynamics.8 The law states: If system A is in thermal equilibrium with system C, and system B is in thermal equilibrium with system C, then systems A and B are in thermal equilibrium with each other.1 In this construction, system C plays the role of a thermometer.13 The profound implication of this law is mathematical: it establishes thermal equilibrium as a transitive relation 9, or more formally, an equivalence relation.14 In mathematics, any equivalence relation partitioning a set of objects implies the existence of a common, scalar property shared by all members of a given equivalence class. The Zeroth Law thus proves the existence of a scalar function of state—a property we call temperature—that is common to all systems in mutual thermal equilibrium.9 The law is, therefore, the fundamental basis for defining temperature and building consistent, reproducible temperature scales.1 This axiomatic foundation also provides the logical origin for one of temperature's most critical characteristics: it is an intensive property. An intensive property is one that does not depend on the size or amount of the system.15 If a large system 'A' is in internal thermal equilibrium 6, any two parts of it, subsystems 'A1' and 'A2', must also be in thermal equilibrium with each other. By the Zeroth Law, a thermometer 'C' that is in thermal equilibrium with the whole system 'A' must also be in thermal equilibrium with 'A1' and 'A2' individually.13 The thermometer, therefore, gives the same reading for all three. This demonstrates that the temperature of a system in thermal equilibrium is the same as the temperature of any part of it.16