Shows Second Law Dynamics of Infinite Quantum Systems with Maximal Entropy Rise

Researchers investigating the fundamental link between quantum dynamics and the second law of thermodynamics present compelling new evidence supporting a deterministic interpretation of entropy increase. Walter F. Wreszinski from the Instituto de Fisica, Universidade de S ao Paulo, alongside colleagues, demonstrate how the dynamics of infinite quantum systems consistently evolve towards increasing mean entropy, ultimately reaching a maximal value. This work significantly advances our understanding by moving beyond probabilistic descriptions of the second law, offering a deterministic theorem specifically for spin systems and illustrating this principle through analysis of the exponential and Dyson models, the latter exhibiting chaotic behaviour. The findings build upon previous work by Albert and Kiessling, providing crucial insight into the behaviour of complex quantum systems and solidifying the connection between microscopic dynamics and macroscopic thermodynamic laws.

The research, led by Walter F. Wreszinski, centres on extending the definition of adiabatic transformation to encompass sudden interactions, thereby generalising the “barrier model”.

This allows for a precise statement of the second law: spontaneous changes in an adiabatically closed system invariably proceed in the direction of increasing mean entropy, ultimately reaching a maximal value. The cornerstone of this theorem lies in the dynamics inducing structural transitions between states of infinite systems over extended timescales, far exceeding typical relaxation times.
Specifically, the study investigates transitions from pure to mixed states within two distinct universality classes of one-dimensional dynamics: the exponential model and the Dyson model. The exponential model, possessing exactly soluble dynamics, does not exhibit a phase transition, providing a baseline for comparison.

Conversely, the Dyson model, lacking exact solutions for both its dynamics and statistical mechanics, demonstrates a ferromagnetic phase transition initially observed by Dyson. Crucially, the team leveraged results from Albert and Kiessling concerning the Cloitre function to reveal strong graphical evidence of chaotic dynamics within the Dyson model.

This discovery establishes a profound distinction in the mechanisms by which these two universality classes approach equilibrium. The approach is dictated exclusively by the underlying dynamics, independent of the initial states or observables. To illustrate this principle, the researchers drew parallels with classical dynamical systems, examining the dyadic map, a simple chaotic system, and its Ruelle-Perron-Frobenius operator.

This analysis demonstrated that while individual orbits within the dyadic map exhibit erratic behaviour, the evolution of densities, functions representing probability distributions, smooths out these irregularities, leading to a predictable approach to equilibrium. The work highlights the importance of defining states not as individual points, but as densities supported by sets of non-zero Lebesgue measure.

Scientists investigated the second law of thermodynamics by developing a deterministic theorem for spin systems, focusing on mean entropy increases in adiabatically closed systems reaching maximal values. The study pioneered a rigorous approach by extending the notion of state to infinite dimensions, essential for precisely defining the second law in a Claudius-like sense.

Researchers began by analysing the dyadic map, T2, defined as T2x = 2x mod 1, operating on the interval [0, 1]. This transformation, while not one-to-one, preserves Lebesgue measure.

Entropy increase and dynamical chaos in infinite-dimensional spin systems are closely linked

Scientists achieved a significant breakthrough in understanding the second law of thermodynamics for spin systems, demonstrating that spontaneous changes in adiabatically closed systems always lead to an increase in mean entropy, eventually reaching a maximal value. The team measured this transition from pure to mixed states in two different universality classes: the exponential model and the Dyson model.

The Dyson models exhibited strong graphical evidence of chaos, as confirmed by Albert and Kiessling’s results on the Cloitre function. Experiments revealed that for large times, the dynamics of the Dyson models are chaotic, differing profoundly from those of the exponential model, which does not display a phase transition.

This distinction highlights how mechanisms of approach to equilibrium vary depending exclusively on the dynamics, rather than the states and observables. The breakthrough delivers a precise statement of the second law in infinite dimensions, emphasizing the importance of generalized states for classical systems.

Entropy increase in spin systems and cosmological implications are deeply connected

Scientists have established a deterministic theorem regarding the second law of thermodynamics for spin systems, refining previous understandings of entropy increase. This research demonstrates that, within adiabatically closed systems, spontaneous changes consistently occur in the direction of increasing mean entropy, ultimately reaching a maximum value.

The work specifically examines transitions from pure to mixed states within one-dimensional systems, focusing on both the exponential and Dyson models, with the latter exhibiting chaotic dynamics. The findings support the notion that the observed prevalence of adiabatic transformations in the Universe is linked to time-reversal invariance, aligning with the hot big-bang theory and its implication of an expanding Universe.

Researchers explored a model incorporating scale-invariance, potentially offering an alternative to the need for dark energy or dark matter assumptions. However, the authors acknowledge limitations in extending this framework to algebraic quantum field theory, particularly concerning the accurate description of ground state energy through perturbation theory, requiring non-perturbative results for further progress. Future research could focus on overcoming these challenges to fully integrate the present framework with AQFT, potentially advancing our understanding of fundamental physical theories like quantum electrodynamics.