Abstract
It was first suggested by David Z. Albert that the existence of a real, physical non-unitary process (i.e., “collapse”) at the quantum level would yield a complete explanation for the Second Law of Thermodynamics (i.e., the increase in entropy over time). The contribution of such a process would be to provide a physical basis for the ontological indeterminacy needed to derive the irreversible Second Law against a backdrop of otherwise reversible, deterministic physical laws. An alternative understanding of the source of this possible quantum “collapse” or non-unitarity is presented herein, in terms of the Transactional Interpretation (TI). The present model provides a specific physical justification for Boltzmann’s often-criticized assumption of molecular randomness (Stosszahlansatz), thereby changing its status from an ad hoc postulate to a theoretically grounded result, without requiring any change to the basic quantum theory. In addition, it is argued that TI provides an elegant way of reconciling, via indeterministic collapse, the time-reversible Liouville evolution with the time-irreversible evolution inherent in so-called “master equations” that specify the changes in occupation of the various possible states in terms of the transition rates between them. The present model is contrasted with the Ghirardi–Rimini–Weber (GRW) “spontaneous collapse” theory previously suggested for this purpose by Albert.
Highlights
Irreversible processes are described by the Second Law of Thermodynamics, the statement that entropy S can never decrease for closed systems: dS
It has been argued that if the non-unitary measurement transition of Von Neumann is a physically real component of quantum theory, the representation of the system(s) under study by proper mixed states, subject to a probabilistic master equation description relative to a distinguished basis, becomes physically justified. This rectifies a weakness in the usual approach, which helps itself to the convenient basis and accompanying probabilistic description [32] as a “for all practical purposes” approximation
The utility of a probabilistic expression for calculational purposes does not constitute theoretical justification for the probabilistic description, which is needed in order for the “coarse-graining” and resulting entropy increase to describe what is physically occurring in a system
Summary
Irreversible processes are described by the Second Law of Thermodynamics, the statement that entropy S can never decrease for closed systems: dS dt ≥ 0. At the quantum level, in order to define the rates of change dPi /dt used in master equations, any phase coherence in quantum states is lost This is a loss of information that can be understood in ontological (rather than epistemic) terms, in contrast to the classical level, if there is ongoing real non-unitary projection into the basis {i}; i.e., repeated transformations of any initial pure state to an epistemic (proper) mixed state. If such non-unitary projection occurs during the evolution of a given system (such as a gas), its entropy does increase, despite the governing deterministic Hamiltonian dynamics; the phase-space conserving evolution of the Liouville equation is physically broken at the micro-level.
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