dorsal/arxiv
View SchemaBrussels-Austin Nonequilibrium Statistical Mechanics in the Early Years: Similarity Transformations between Deterministic and Probabilistic Descriptions
| Authors | Robert C. Bishop |
|---|---|
| Categories | |
| ArXiv ID | physics/0304018 |
| URL | https://arxiv.org/abs/physics/0304018 |
Abstract
The fundamental problem on which Ilya Prigogine and the Brussels-Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like Uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of time was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels-Austin Group, is to consider the observed direction of time to be a basics physical phenomenon and to develop a mathematical formalism that can describe this direction as being due to the dynamics of physical systems. In part I of this essay, I review and assess an attempt to carry out an approach that received much of their attention from the early 1970s to the mid 1980s. In part II, I will discuss their more recent approach using rigged Hilbert spaces.
{
"annotation_id": "8c817108-93a0-46b0-a15f-532a63d8373d",
"date_created": "2026-03-02T18:00:42.339000Z",
"date_modified": "2026-03-02T18:00:42.339000Z",
"file_hash": "7de624677266793d1b99b4b1be753c02dcc3085254115d2b0e8af3433bb9830d",
"private": false,
"record": {
"abstract": "The fundamental problem on which Ilya Prigogine and the Brussels-Austin Group\nhave focused can be stated briefly as follows. Our observations indicate that\nthere is an arrow of time in our experience of the world (e.g., decay of\nunstable radioactive atoms like Uranium, or the mixing of cream in coffee).\nMost of the fundamental equations of physics are time reversible, however,\npresenting an apparent conflict between our theoretical descriptions and\nexperimental observations. Many have thought that the observed arrow of time\nwas either an artifact of our observations or due to very special initial\nconditions. An alternative approach, followed by the Brussels-Austin Group, is\nto consider the observed direction of time to be a basics physical phenomenon\nand to develop a mathematical formalism that can describe this direction as\nbeing due to the dynamics of physical systems. In part I of this essay, I\nreview and assess an attempt to carry out an approach that received much of\ntheir attention from the early 1970s to the mid 1980s. In part II, I will\ndiscuss their more recent approach using rigged Hilbert spaces.",
"arxiv_id": "physics/0304018",
"authors": [
"Robert C. Bishop"
],
"categories": [
"physics.class-ph",
"physics.gen-ph"
],
"title": "Brussels-Austin Nonequilibrium Statistical Mechanics in the Early Years: Similarity Transformations between Deterministic and Probabilistic Descriptions",
"url": "https://arxiv.org/abs/physics/0304018"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "8ac0ffb1-ec57-4750-8599-ae8aa063a20a",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}