Entropy, Extropy and the Physical Driver of Irreversibility (original) (raw)
Related papers
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
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.
Rethinking the Concept of Entropy
2019
It is shown that the construction of thermodynamics with a focus directly on nonequivalent systems leads to the understanding of entropy as a “thermoimpulse” — the impulse of internal motion that has lost its vector nature due to its chaos. Unlike entropy, thermoimpulse allows its diminution in adiabatic processes, which eliminates the contradiction of the principle of its increase to the laws of evolution, the threat of the “thermal death of the Universe”, Gibbs paradoxes, absolute temperatures, relativistic heat engines, etc., leaving it unshakable experimentally established laws.
Entropy and irreversibility in dynamical systems
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2013
A method of defining non-equilibrium entropy for a chaotic dynamical system is proposed which, unlike the usual method based on Boltzmann’s principle , does not involve the concept of a macroscopic state. The idea is illustrated using an example based on Arnold’s ‘cat’ map. The example also demonstrates that it is possible to have irreversible behaviour, involving a large increase of entropy, in a chaotic system with only two degrees of freedom.
The irreversibility and classical mechanics laws
2004
The irreversibility of the dynamics of the conservative systems on example of hard disks and potentially of interacting elements is investigated in terms of laws of classical mechanics. The equation of the motion of interacting systems and the formula, which expresses the entropy through the generalized forces, are obtained. The explanation of irreversibility mechanism is submitted. The intrinsic link between thermodynamics and classical mechanics was analyzed. Introduction. Irreversibility determines the contents of the second law of thermodynamics in fundamental physics. According to this law there is function S named entropy, which only grows for isolated systems, achieving a maximum in an equilibrium state. But the potentiality of forces for all four known fundamental interactions of elementary particles is a cause of reversibility of the Newton equation [1] and therefore
Physics of the Solid State, 2019
It is shown that retardation of the interactions between particles leads to the nonexistence of potential energy and the Hamiltonian of the particle system. This leads to the impossibility of calculating the thermodynamic functions of the system by the methods of statistical mechanics. The dynamics of a system of particles with delayed interactions is described by a system of functional differential equations. The qualitative properties of the solutions of this system of equations are investigated. The solutions are irreversible with respect to time reversal. The number of degrees of freedom of even a finite system with retarded interactions is infinite.
1997
Boltzmann's 1872 derivation of the H-theorem was of great significance because it provided a basis for the second law of thermodynamics in terms of the molecular/kinetic theory of heat. By showing that a statistical treatment of the many molecules comprising a gas can produce a monotonic decrease of an entropy-like quantity, H ~ -S , he provided the essential insight into the connection between the second law and the evolution of systems through macroscopic states occupying progressively larger volumes in phase space. However, it is a common misconception that an analysis like that given by Boltzmann demonstrates that the second law of thermodynamics would be observed in a universe of particles whose motions are completely described by the laws of classical mechanics. I attempt to clarify that this is a misconception by showing that an element introduced into Boltzmann's derivation as simply an approximation to the dynamics expected under classical mechanics, in fact introduces a new feature into the dynamics of the model system. It is shown that this added feature, present in the model but not in a classical mechanical universe, is solely responsible for the monotonic behavior of H. Hence, while this type of analysis provides an understanding of how the second law comes about, it does not stay within the confines of classical mechanics in doing so. Thus it is not a derivation of the second law of thermodynamics just from the laws of classical mechanics for a system with many degrees of freedom and a low-entropy initial condition. The implications of this conclusion are important for our understanding of the physical basis of the second law of thermodynamics.
The relation between macroscopic irreversibility and microscopic reversibility is a present unsolved problem. Constructal law is introduced to develop analytically the Einstein's, Schrödinger's, and Gibbs' considerations on the interaction between particles and thermal radiation (photons). The result leads to consider the atoms and molecules as open systems in continuous interaction with flows of photons from their surroundings. The consequent result is that, in any atomic transition, the energy related to the microscopic irreversibility is negligible, while when a great number of atoms (of the order of Avogadro's number) is considered, this energy related to irreversibility becomes so large that its order of magnitude must be taken into account. Consequently, macroscopic irreversibility results related to microscopic irreversibility by flows of photons and amount of atoms involved in the processes. In 1872, Boltzmann summarized his statistical mechanical results in his famous H-theorem. He introduced the irreversible evolution of any system towards a state of mechanical and thermal equilibrium. Loschmidt objected that this result is inconsistent, because any irreversible process cannot be obtained by using a time-symmetric dynamics 1. This controversy is no more than the problem of the link between the microscopic reversibility and the mac-roscopic irreversibility, named Loschmidt paradox. Despite the enormous advances of statistical mechanics in the description of equilibrium properties and transport processes in condensed matter, the problem of the non-contradictory microscopic foundation of both thermodynamics and kinetics remains unsolved 1. The analytical study of macroscopic irreversibility comes since 1789, when Benjamin Thompson (Count Rumford) highlighted that heat could be generated by friction 2. In 1803, Lazare Carnot analyzed the conservation of mechanical energy for pulleys and inclined planes, pointing out that, in any movement, there always exists a loss of " moment of activity " 3. But, the thermodynamic interpretation of this irreversibility was introduced first in 1824 by his son Sadi Carnot, who introduced the concept of the ideal engine, which is an ideal system which operates on a cycle in a completely reversible way, without any dissipation: unfortunately, efficiency of this ideal systems has an upper limit and isn't unitary. Surprisingly, even in ideal condition without any dissipation, there is something that prevents the conversion of all the energy absorbed, from an ideal reservoir, into work 4. This result was improved, in 1852, by Lord Kelvin, who pointed out that 5,6 :
Phenomenological thermodynamics and entropy principles
2003
There is no unified approach to irreversible thermodynamics in the phenomenological theories of continuum thermodynamics. The different approaches are based on different forms of the second law. Depending upon which basic underlying principles are postulated, the entropy principle yields different implications on the nonequilibrium quantities for these to fulfil the irreversibility requirements.