Concept ambitious, details elusive

I. Framework

Prigogine's pathway to irreversibility and dissipative structure can be summarized as follows:

1. Microscopic reversibility

At the microscopic scale, individual particle dynamics are deterministic and time-reversible, as governed by Newton's equations or Schrödinger's equation.

2. Emergence of irreversibility

In interacting many-particle systems, Poincaré resonances dynamically arise during collisions or interactions. These resonances:

(i) introduce effective stochasticity in particle trajectories -> microscopic indeterminism, and

(ii) drive irreversible delocalization of the phase-space distribution -> macroscopic irreversibility.

3. Selection of irreversible processes

The specific irreversible path adopted depends on the system's distance from equilibrium:

(i) Near equilibrium (small driving forces): Systems evolve toward the steady-state process with the minimum entropy production rate.

(ii) Far from equilibrium (large driving forces): Nonlinear effects create multiple stable branches in the entropy production landscape. Each branch corresponds to a dissipative structure. Selection among these states depends on: initial conditions and the relative size of basins of attraction in phase space.

II. Debate

The paradox that how macroscopic irreversibility emerges from microscopic reversible laws remains a topic in the foundations of physics. While Prigogine offers a compelling framework, his explanation is not the prevailing view today. The mainstream today is the Boltzmann’s entropy-based explanation, which Prigogine critiques in Chapter 1, Epicurus’ Dilemma.

A commonly cited counterexample involves a system of non-interacting particles initially confined to one half of a chamber. Over time, the particles spread out uniformly. This phenomenon can be explained by the statistical dominance of high-entropy states: Phase space contains vastly more microstates where particles are spread out than where they are initially confined.

Does this example imply that interactions (and thus Poincaré resonances) are not necessary for irreversibility? Prigogine argues this is NOT truly reversibility.

(i) The process "looks" irreversible because we can only observe coarse-grained properties, e.g., the number of molecules. If we could track each particle's trajectory, we would see a time-reversible process. The irreversibility for this particle spreading process is just a consequence of the approximation in our observation, not a basic law.

(ii) According to the Poincaré recurrence theorem, "if we were to wait long enough, we could observe the spontaneous return of a dynamical system to a state as close to the initial state as we might wish". So, the initial confined state can be viewed as a snapshot in an equilibrium fluctuation, rather than an irreversible process.

For Prigogine, the particle spreading process is reversible. But, there indeed exist really irreversible processes. In far-from-equilibrium conditions, people observe phenomena like the spontaneous formation of ordered patterns, which cannot be explained by the entropy argument. These observations suggest that the arrow of time can be a source of order, motivating the need for a theory of intrinsic irreversibility, where Poincaré resonances play a central role.

Thermodynamics and Boltzmann’s statistical framework still work well for many practical problems. That's why they dominate the mainstream today. However, I believe, as research increasingly explores far-from-equilibrium regimes, Prigogine’s theory -- centered on intrinsic irreversibility and Poincaré resonances -- may gain broader relevance. Perhaps we are already in such regimes, but not yet fully prepared to adopt Prigogine’s approach.