This paper views canonical distribution as the consequence of subquantum processes. It is these processes that lead to the macrosystem’s irreversible evolution towards the maximum freedom in realizing its state, i.e. towards maximum entropy. The paper presents a formula which connects the macrosystem’s entropy with the maximum number of its state realizations as a consequence of subquantum processes.
This paper views canonical distribution as the consequence of subquantum processes. It is these processes that lead to the macrosystem’s irreversible evolution towards the maximum freedom in realizing its state, i.e. towards maximum entropy. The paper presents a formula which connects the macrosystem’s entropy with the maximum number of its state realizations as a consequence of subquantum processes.
This paper critically considers the main interpretations of the wave function and offers an interpretation in which wave function is a consequence of subquantum processes taking place at the level of the organization of matter which underlies the phenomena described by quantum mechanics. We show that this interpretation provides a common ground to explain problematic issues of quantum theory (wave function collapse, electrons passing through two slits, behavior of electrons within the atom, quantum entanglement). The paper also shows that entropy is determined by the maximum number of macrosystem states which appear as the result of subquantum processes.
The paper examines and critiques the expression of entropy as the logarithm of the number of quantum states of a physical system. Boltzmann method of expressing entropy as the logarithm of the number of states of a gas with a given total energy is analyzed. We demonstrate that entropy is the product of subquantum processes and show that entropy is expressed as the ratio of the logarithm of the maximum number of realizations, over the observation period, of a macroscopic system's states with a given total energy, to the number of occurrences of its quantum states over this time.
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
We show insurmountable contradictions which arise if statistical ensembles are considered a consequence of the influence of the environment of the physical systems. We regard the multiplicity of states with a definite energy value as a result of internal probabilistic processes in the macrosystem; these internal probabilistic processes are not taken into account by quantum mechanics. On a simple example it is demonstrated, that canonical distribution is not independent and equal to microcanonical one, but is a result of averaging by microcanonical ensemble.
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability distribution {p(j∣K)} for states labelled by j given data K implies that the corresponding maximal value of the information entropy σ({(pj∣K)})=−∑j(pj∣K)ln(pj∣K) depends explicitly on the data at equilibrium and on the Hamiltonian of the system. As such, it is a direct measure of our uncertainty about the exact state of the body and can be identified with the traditional thermodynamic entropy. We consider the well known microcanonical, canonical and grand canonical methods and ensure that the fluctuations about mean values are generally minuscule for macroscopic systems before identifying these mean values with experimental observables and thereby connecting to many standard results from thermodynamics. Unexpectedly, we find that it is not generally possible for a quantum process to be both isentropic and reversibly adiabatic. This is in sharp contrast to traditional thermodynamics where it is assumed that isentropic, reversible adiabatic processes can be summoned up on demand and easily realised. By contrast, we find that linear relations between pressures Pj and energies Ej are necessary and sufficient conditions for a quasi-static and adiabatic change to be isentropic, but, of course, this relationship only holds for a few especially simple systems, such as the perfect gas, and is not generally true for more complicated systems. By considering the associated entropy increases up to second order in small volume changes we argue that the consequences are in practice negligible.
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.