The Arrow of Time and Its Irreversibility

Quantum thermodynamics strives to extend classical thermodynamics and nonequilibrium statistical physics to ensembles of sizes below the thermodynamic limit with the full inclusion of quantum e ﬀ ects. This paper uses the nonrelativistic quantum mechanics of a lone system in a thermal bath to relate its wave function’s local phase to Lorentz-Faraday forces acting thereon. In the intake of heat from its surroundings, such a system’s entropy increases with the gain connected to the gradient ﬁeld of its local phase whose subharmonicity within the boundary of its volume is a necessary and su ﬃ cient condition for it to comply with the second law of thermodynamics (SLT). The thermodynamic arrow of time necessitates irreversible over reversible processes as determined by the gradient ﬁeld of the phase. Conservative Lorentz-Faraday forces identiﬁed herein impress on the system to engender irreversible (reversible) change and entropy gain (stasis) in its exchange of heat with its environment under the discernment of the thermodynamic arrow of time and regardless of the time-reversal symmetry of such venerable frameworks as electrodynamics and quantum mechanics. Entropy production is greatest when the local phase is subharmonic within the system’s nominal volume. A means of time-averaging entropy and free energy changes under nonstandard-state conditions with the accommodation of phenomenological relaxation is provided. Both the SLT and Faraday’s law of induction are of similar vintage and status. Surprisingly, they share a hitherto unrecognized connection at the microscopic level. Faraday’s law of induction is shown to hold for a lone system provided the gradient of its local phase is ﬁnite, a necessary and su ﬃ cient condition for it not to present with its alleged paradoxes and contradictions despite its technological successes rivalling those of the SLT. There is no evidence to deny the successes of both the SLT and Faraday’s law for science and technology. In compliance with Earnshaw’s theorem, the potential of the Lorentz-Faraday force is shown to stabilize a lone system just like the Coulomb (or Newtonian) potential while continuing to fulﬁll the virial theorem. A consequence of the time asymmetry of entropy is the impossibility of travel to the past as to cause entropy changes to decrease contrary to the SLT. Further consequences of entropy’s time asymmetry include at least the nonexistence of magnetic monopoles, the observed matter-antimatter asymmetry in leptonic and baryonic matter, and the role of axion-like particles in accounting for the absence of charge-parity violations in strong interactions without necessarily answering for dark matter. Within the range of validity of gravito(electro)magnetism, dark energy is identiﬁed as the work done by the Heaviside analog of the Lorentz-Faraday force in causing the accelerated expansion of the Universe without reference to either a ﬁnite cosmological constant or an unstable vacuum state transition. In the practice of reduc-tionism, macroscopic physics supervenes upon the microscopic, the SLT being the most conspicuous exception to that superﬂuous tenet. The supersedence of classical thermo-dynamics over quantum mechanics and electrodynamics across spatio-temporal scales ranging from an individual quantized system to its known Universe has been shown herein. Additionally, in showing that reversible (irreversible) processes are a ﬃ liated with the particle (wave) behavior of matter, attention has been drawn to a heretofore overlooked connection between the di ﬀ erent roles of classical thermodynamics and quantum mechanics and electrodynamics in respect to arrow-of-time asymmetry and wave-particle duality.