Irreversibility and the arrow of time (original) (raw)
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Aapp Physical Mathematical and Natural Sciences, 2008
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 questions is given by Statistical Mechanics. Indeed, for everyday laboratory physics, the mathematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions) allows a successful description of the thermodynamic equilibrium properties of matter, including entropy values. However, as already 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 into the laws of microscopic physics. The result is a theory, that we call Quantum Thermodynamics, that has all the necessary features to combine Mechanics and Thermodynamics uniting all the successful results of both theories, eliminating the logical inconsistencies of Statistical Mechanics and the paradoxes on irreversibility, and providing an entirely new perspective on the microscopic origin of irreversibility, nonlinearity (therefore including chaotic behavior) and maximal-entropy-generation nonequilibrium dynamics. 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, including Onsager reciprocity relations and maximal-entropy-generation nonequilibrium dynamics, which we believe provides the microscopic foundations of heat, mass and momentum transfer theories, including all their implications such as Bejan's Constructal Theory of natural phenomena.
arXiv (Cornell University), 2021
All the laws of physics are time-reversible. Time arrow emerges only when ensembles of classical particles are treated probabilistically, outside of physics laws, and the entropy and the second law of thermodynamics are introduced. In quantum physics, no mechanism for a time arrow has been proposed despite its intrinsic probabilistic nature. In consequence, one cannot explain why an electron in an excited state will "spontaneously" transition into a ground state as a photon is created and emitted, instead of continuing in its reversible unitary evolution. To address such phenomena, we introduce an entropy for quantum physics, which will conduce to the emergence of a time arrow. The entropy is a measure of randomness over the degrees of freedom of a quantum state. It is dimensionless; it is a relativistic scalar, it is invariant under coordinate transformation of position and momentum that maintain conjugate properties and under CPT transformations; and its minimum is positive due to the uncertainty principle. To excogitate why some quantum physical processes cannot take place even though they obey conservation laws, we partition the set of all evolutions of an initial state into four blocks, based on whether the entropy is (i) increasing but not a constant, (ii) decreasing but not a constant, (iii) a constant, (iv) oscillating. We propose a law that in quantum physics entropy (weakly) increases over time. Thus, evolutions in the set (ii) are disallowed, and evolutions in set (iv) are barred from completing an oscillation period by instantaneously transitioning to a new state. This law for quantum physics limits physical scenarios beyond conservation laws, providing causality reasoning by defining a time arrow.
Irreversible entropy production: From classical to quantum
Reviews of Modern Physics, 2021
Entropy production is a key quantity in any finite-time thermodynamic process. It is intimately tied with the fundamental laws of thermodynamics, embodying a tool to extend thermodynamic considerations all the way to non-equilibrium processes. It is also often used in attempts to provide the quantitative characterization of logical and thermodynamic irreversibility, stemming from processes in physics, chemistry and biology. Notwithstanding its fundamental character, a unifying theory of entropy production valid for general processes, both classical and quantum, has not yet been formulated. Developments pivoting around the frameworks of stochastic thermodynamics, open quantum systems, and quantum information theory have led to substantial progress in such endeavour. This has culminated in the unlocking of a new generation of experiments able to address stochastic thermodynamic processes and the impact of entropy production on them. This paper aims to provide a compendium on the current framework for the description, assessment and manipulation of entropy production. We present both formal aspects of its formulation and the implications stemming from the potential quantum nature of a given process, including a detailed survey of recent experiments.
Irreversibility, the time arrow and a dynamical proof of the second law of thermodynamics
Quantum Studies: Mathematics and Foundations
We provide a dynamical proof of the second law of thermodynamics, along the lines of an argument of Penrose and Gibbs, making crucial use of the upper semicontinuity of the mean entropy proved by Robinson and Ruelle and Lanford and Robinson. An example is provided by a class of models of quantum spin systems introduced by Emch and Radin. Consequences regarding irreversibility and the time arrow, as well as possible extensions to quantum continuous systems, are discussed.
Quantum causality and the arrows of time and thermodynamics
Progress in Particle and Nuclear Physics, 2020
In the understanding of the fundamental interactions, the origin of an arrow of time is viewed as problematic. However, quantum field theory has an arrow of causality, which tells us which time direction is the past lightcone and which is the future. This direction is tied to the conventions used in the quantization procedures. The different possible causal directions have related physics-in this sense they are covariant under time-reversal. However, only one causal direction emerges for a given set of conventions. This causal arrow tells us the direction that scattering reactions proceed. The time direction of scattering in turn tells us the time direction for which entropy increases-the so-called arrow of thermodynamics. This connection is overlooked in most discussions of the arrow of time.
Reversibility and Irreversibility within the Quantum Formalism
The discussion on time-reversal in quantum mechanics exists at least since Wigner's paper in 1932. If and how the dynamics of the quantum world is time-reversible has been the subject of many controversies. Some have seen quantum mechanics as fundamentally time-irreversible, see for example von Neumann [16, p. 358], and some have seen in that the ultimate cause of time's arrow and second law behavior. In his best-selling book, Roger Penrose argues similarly and concludes that "our sought-for quantum gravity must be a time-asymmetric theory" [13, p. 351]. In a recent issue of Physicalia, [5], we read yet about another project: to extend quantum mechanics into new fundamentally irreversible equations, thus proposing a new theory giving "... une description fondamentale irréversible de tout système physique". It is that last paper that has triggered our writing of the present contribution.
The path information required for microscopic reversibility of particle paths is destroyed or erased by local interactions with radiation and other particles. Ludwig Boltzmann's dynamical H-Theorem (his 1872 Stosszahlansatz) correctly predicts the approach to equilibrium. But this apparent increase in entropy can be reversed, according to Josef Loschmidt's time-reversibility objection and Ernst Zer-melo's recurrence objection. We show that the addition of electromagnetic radiation adds an irreducible element of randomness to atomic and molecular motions, erasing classical path information, just as the addition of a small speck of material can thermalize a non-equilibrium radiation field. Path erasure prevents reversibility and maintains a high entropy state indefinitely. Statistical fluctuations from equilibrium are damped by path erasure. Photon emission and absorption during molecular collisions is shown to destroy nonlocal molecular correlations, justifying Boltzmann's assumption of " molecular chaos " (molekular ungeordnete) as well as Maxwell's earlier assumption that molecular velocities are not correlated. These molecular correlations were retained in Willard Gibbs formulation of entropy. But the microscopic information implicit in classical particle paths (which would be needed to implement Loschmidt's determin-istic motion reversal) is actually erased, justifying what N. G. van Kampen calls a " repeated randomness " assumption. Boltzmann's physical insight was correct that his increased entropy is irreversible. It has been argued that photon interactions can be ignored because radiation is isotropic and thus there is no net momentum transfer to the particles. The radiation distribution, like the distribution of particles, is indeed statistically isotropic, but, as we show, each discrete quantum of angular momentum exchanged during individual photon collisions alters the classical paths sufficiently to destroy molecular velocity correlations. Path erasure is a strong function of temperature, pressure, and the atomic and molecular species of the gas. We calculate path erasure times over a range of conditions , from standard temperature and pressure to the extreme low densities and temperatures of the intergalactic medium. Reversibility is closely related to the maintenance of path information forward in time that is required to assert that physics is deterministic. Indeterministic interactions between matter and radiation erase that path information. The elementary process of the emission of radiation is not time reversible, as first noted by Einstein in 1909. Macroscopic physics is only statistically determined. Macroscopic processes are adequately determined when the the mass m of an object is large compared to the Planck quantum of action h (when there are large numbers of quantum particles). But the information-destroying elementary processes of emission and absorption of radiation ensure that macroscopic processes are not reversible. 2
Irreversible Work and Inner Friction in Quantum Thermodynamic Processes
Physical Review Letters, 2014
We discuss the thermodynamics of closed quantum systems driven out of equilibrium by a change in a control parameter and undergoing a unitary process. We compare the work actually done on the system with the one that would be performed along ideal adiabatic and isothermal transformations. The comparison with the latter leads to the introduction of irreversible work, while that with the former leads to the introduction of inner friction. We show that these two quantities can be treated on equal footing, as both can be linked with the heat exchanged in thermalization processes and both can be expressed as relative entropies. Furthermore, we obtain a fluctuation relation for the entropy production associated with the inner friction. PACS numbers: 05.70.Ln, 05.30-d