Hatsopoulos and Gyftopoulos (1976a,b,c,d) founded the Unified Quantum Theory of Mechanics and Thermodynamics. This theory encompasses both quantum mechanics and thermodynamics within a single mathematical framework. Unlike statistical approaches, it treats thermodynamics as a non-statistical (hence, a physical) theory and is intended to describe all reversible and irreversible phenomena. Unfortunately, the theory has long been criticized for not bringing anything new beyond statistical quantum thermodynamics. To break through this misconception that thermodynamics is a statistical theory, experimental validation at a microscopic scale, where statistical effects are negligible, would be fruitful. In this paper, which is based on the dissertation work of the author (1993), experiments that were previously reported are investigated within the framework of the new theory. It is argued that they provide an undeniable confirmation of the theory and the existence of irreversibility at the microscopic scale.An initial version of this paper was published inJuly of 2006 in the proceedings of ECOS’06, AghiaPelagia, Crete, Greece.
Hatsopoulos and Gyftopoulos (1976a,b,c,d) founded the Unified Quantum Theory of Mechanics and Thermodynamics. This theory encompasses both quantum mechanics and thermodynamics within a single mathematical framework. Unlike statistical approaches, it treats thermodynamics as a non-statistical (hence, a physical) theory and is intended to describe all reversible and irreversible phenomena. Unfortunately, the theory has long been criticized for not bringing anything new beyond statistical quantum thermodynamics. To break through this misconception that thermodynamics is a statistical theory, experimental validation at a microscopic scale, where statistical effects are negligible, would be fruitful. In this paper, which is based on the dissertation work of the author (1993), experiments that were previously reported are investigated within the framework of the new theory. It is argued that they provide an undeniable confirmation of the theory and the existence of irreversibility at the microscopic scale.An initial version of this paper was published inJuly of 2006 in the proceedings of ECOS’06, AghiaPelagia, Crete, Greece.
Thermodynamics is the science that deals with all the phenomena that involve the transfer of energy, i.e. heat and work. Its development started in 1824 with the efforts of Sadi Carnot to improve the closed-cycle steam engine discovered by James Watt in 1764. In 1850, R. Clausius laid the foundations of the laws of thermodynamics. Soon thereafter a conflict between the second law of Thermodynamics and the laws of mechanics was pointed out by Maxwell in 1871 and was illustrated clearly by what has come to be known as Maxwell’s demon. This conflict was addressed by Brillouin (1949) based on the work of Szilard (1929) and of many others. They all claimed that although the objective state of a system is fully describable by mechanics, classical or quantum, and evolves according to the laws of mechanics, some states of the system as perceived by an observer are subjective and reflect the lack of information the observer has about the actual mechanical state of the system. This point of view is, in effect, the information-theory interpretation of thermodynamics which, currently, is widely accepted. The central point of this paper is to describe the reasons why the information-theory interpretation of thermodynamics is contrary to physical reality. It shows that a logically viable hypothesis which reconciles mechanics with thermodynamics is the existence in nature of physical states that have objective uncertainties broader than those implied in quantum theory as it is traditionally formulated. The consequences of this hypothesis are presented in the Unified Quantum Theory of Mechanics and Thermodynamics, by Hatsopoulos and Gyftopoulos.An initial version of this paper was published inJuly of 2006 in the proceedings of ECOS’06, AghiaPelagia, Crete, Greece.
The author presents his experience in teaching at a graduate level the quantal exposition of a new non-statistically based paradigm of physics and thermodynamics. This paradigm, called the Unified Quantum Theory of Mechanics and Thermodynamics, applies to all systems large or small (including one particle systems) either in a state of thermodynamic (i.e. stable) equilibrium or not in a state of thermodynamic equilibrium. It uses as its primitives inertial mass, force, and time and introduces the laws of thermodynamics in the most unambiguous and general formulations found in the literature. Starting with a precise definition of system and of state followed by statements and corollaries of the laws of thermodynamics, the thermodynamic formalism is developed without circularity and ambiguity. In this quantal exposition of the new paradigm, a brief review of the formalism of thermodynamics as a general science not limited to stable equilibrium and large (macroscopic) systems as well as a very brief summary of the three prevalent formalisms in classical physics are presented followed by a presentation and development of solutions for a number of elementary problems in quantum physics (e.g., a particle in a box, a harmonic oscillator, a rigid rotor, etc.). These solutions and the maximum entropy principle are then used in a constrained optimization to develop the canonical and grand canonical distributions for Fermi-Dirac and Bose-Einstein types of particles, i.e. for fermions and bosons. This is done without the use of analogies between statistical and thermodynamic results and without additional hypotheses such as the ergodic hypothesis of statistical mechanics. These distributions are then employed under various assumptions (i.e. the Boltzmann, constant-potential, point-particle, and continuous eigenvalue-spectrum approximations) to derive the corresponding thermodynamic property expressions for perfect, semi-perfect (ideal), and Sommerfeld gases as well as for mixtures of ionized and dissociated gases. In a similar fashion but with a change from a single- to a multi-particle partition function and with the addition of various inter-particle potentials for two-particle interactions (e.g., the Lennard-Jones potential, the square-well potential, etc.), expressions for the thermodynamic properties of dense gases are developed and presented.An initial version of this paper was published inJuly of 2006 in the proceedings of ECOS’06, AghiaPelagia, Crete, Greece.
ABSTRACT. What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? Most physicists still accept and teach that the rationalization of these fundamental ques-tions is given by Statistical Mechanics. Indeed, for everyday laboratory physics, the math-ematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions) allows a successful description of the ther-modynamic equilibrium properties of matter, including entropy values. However, as al-ready recognized by Schrödinger in 1936, Statistical Mechanics is impaired by conceptual ambiguities and logical inconsistencies, both in its explanation of the meaning of entropy and in its implications on the concept of state of a system. An alternative theory has been developed by Gyftopoulos, Hatsopoulos and the present author to eliminate these stumbling conceptual blocks while maintaining the mathematical formalism so successful in applications. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility we have built entropy and irreversibility
Basing his work on a new formulation of thermodynamics called the Unified Quantum Theory of Mechanics and Thermodynamics first published in a series of four ground breaking papers in 1976 (Hatsopoulos and Gyftopoulos, 1976a, b, c, d), Beretta develops a dynamical postulate (Beretta et al. 1984; Beretta, Gyftopoulos, and Park, 1985) consistent both with the non-dynamical quantum mechanical postulates of the Unified Theory as well as with its thermodynamic ones (the 2nd Law in particular). The theory itself simply and elegantly extends in a unified fashion the concepts of thermodynamics to quantum mechanics and the concepts of quantum mechanics to thermodynamics. It does so without the bridge traditionally used, i.e. statistical mechanics, eliminating a number of the ambiguities, tautologies, and inconsistencies (including a built-in violation of the 2nd Law) inherent in the presentations of both Classical and Statistical Thermodynamics. This new formulation generalizes thermodynamics so that it applies to all systems large or small (including one particle systems) either in a state of thermodynamic (i.e. stable) equilibrium or not in a state of thermodynamic equilibrium. The Beretta equation of motion describes the time evolution of the state of a system via a density operator which is uniquely based on an unambiguous preparation of an ensemble of identical systems, i.e. the so-called homogenous or irreducible ensemble, and does so both for unitary and non-unitary reversible as well as irreversible processes. In this paper, we present a simple application of this general equation of motion to the time evolution of the entropy of a closed system comprised of a Boltzmann type gas consisting of one or of many particles undergoing an irreversible process. A number of different energy eigenlevels and initial states and their effects on entropy generation and the final state of maximum entropy, i.e. stable equilibrium, are examined. A simple time-dependent work interaction is introduced into the formulation to show how this in turn affects the evolution of the state of the system.
Abstract The transition from microscopic reversible dynamics to macroscopic irreversible thermodynamics in statistical mechanics, the transformation from pure states to mixed states during quantum decoherence, and the transition from quantum superposition states to classical definite states in quantum measurement have long been regarded as three independent fundamental physical puzzles. This paper demonstrates that the three processes share a unified mathematical root: the filtering, truncation or projection of system degrees of freedom renders the information carried by partial degrees of freedom unreconstructable within the reduced description framework, and irreversibility spontaneously emerges in the remaining description space. Based on the rigorous derivation of Hilbert’s sixth problem proposed by Deng et al., Zurek’s environment-induced decoherence theory, and the three-stage model of temporal relativity proposed by the author, this paper extracts the mathematical structure of the three types of physical processes and constructs an axiomatic unified framework. This paper further clarifies that various filtering operations are essentially equivalent to the selection of reference frames by the observation system; any descriptive subject with finite information bandwidth must select a reference benchmark, and the arrow of time is an emergent characteristic of this selection behavior under reduced description. This paper distinguishes between global information conservation and local unreconstructable information, emphasizing that the theoretical framework does not violate unitary quantum evolution, and proposes quantitative predictions verifiable by attosecond physics and superconducting quantum experiments.
What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? The bulk of the physics community accepts and teaches that all these fundamental questions are rationalized within statistical mechanics. Indeed, for everyday laboratory physics, the mathematical formalism of statistical mechanics (canonical and grandcanonica1, Boltzmann, Bose-Einstein and Fermi-Dirac distributions) allows a successful description of the thermodynamic equilibrium properties of matter, including entropy values. But an ever growing handful of physicists (Schrodinger among the first) have realized that, even in its explanation of the meaning of entropy, statistical mechanics is impaired by ambiguities and logical inconsistencies. They have started to search for a better theory to eliminate these stumbling blocks while maintaining the mathematical formalism that has been so successful in so many applications. This handful of upstreamers must not be confused with the many schools of physicists that have thrived on the more renowned incompleteness of statistical mechanics, namely, the lack of a quantitative (and the weakness of the qualitative) explanation of the origin of irreversibility. In these studies the thrust is provided by the discovery that the macroscopic dynamics of certain complex systems may be modeled using a few-degrees-of-freedom nonlinear Hamiltonian with singularities that give rise to bifurcations and chaotic behavior. These results have generated successful ways to describe irreversible behavior, but their link to the origin of irreversibility is still only heuristic (what is the connection between the nonlinear model Hamiltonian and the true full Hamiitonian?) and does not provide yet a rigorous resolution of the century-old paradox of the conflict between the irreversibiiity of macroscopic behavior, and the reversibility of the laws of mechanics. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility we have built entropy and irreversibility into the laws of mechanics. The result is a theory that we call quantum thermodynamics that has all the necessary properties to combine mechanics and thermodynamics uniting all the successful results of both theories, eliminating the logical inconsistencies of statistical mechanics and the paradox on irreversibiiity, and providing an entirely new perspective on the microscopic origin of irreversibility, nonlinearity and therefore chaotic behavior. The mathematical formalism of quantum thermodynamics differs from that of statistical mechanics mainly in the equation of motion which is nonlinear but has solutions identical to those of the Schrodinger equation for all the states for which statistical mechanics reduces to quantum mechanics. The physical meaning of the formalism of quantum thermodynamics differs more drastically from that of statistical mechanics. The significance of the state operator of quantum thermodynamics is entirely different from that of the density operator of statistical mechanics, even though the two are mathematically equivalent. Indeed they obey different equations of motion. In particular, quantum thermodynamics is concerned only with those systems for which quantum mechanics would describe the states with vectors in Hilbert space or, equivalently, projection operators. Using a well known jargon, we can say that quantum thermodynamics like quantum mechanics is concerned only with pure quantum states. However, it postulates that the set of pure quantum states of a system is much broader than contemplated by quantum mechanics. Pure quantum states must be described by operators defined by all the features of projection operators except the condition of idempotence. As a result, an operator that within statistical mechanics would describe a mixed quantum state (that is, the average state of a statistical mixture of identical systems in different pure quantum states) in quantum thermodynamics describes a pure quantum state, a state that neither quantum mechanics non statistical mechanics would contemplate. Conceptually, the increased richness of pure quantum states is a new revolutionary postulate of quantum physics. But from the point of view of the statistical mechanics practitioners the new theory is not as traumatic as it seems. Whenever one uses a nonidempotent density operator to describe a thermodynamic equilibrium state one simply has to reinterpret it as one of the new pure quantum states. One even saves the usual ad hoc arguments on thermal baths and reservoirs that are usually required in statistical mechanics to justify the use of a nonidempotent density operator to describe the state of a system. In this paper we discuss the background and formalism of quantum thermodynamics including its nonlinear equation of motion and the main general results. Our objective is to show in a not-too-technical manner that this theory provides indeed a complete and coherent resolution of the century-old dilemma on the meaning of entropy and the origin of irreversibility. As a byproduct, we discuss a long set of criteria that a theory should meet in order to afford the same claim.