Information Loss and an Intrinsic Arrow of Time

Definitions and mathematical statement

The supplied record concerns an intrinsic arrow of time, a group description of time, uncertainty about the past, and information loss concerning properties of states. It does not define these notions mathematically: no state space, time group, evolution law, observation model, uncertainty measure, or information functional is specified. In particular, it is unclear whether the proposed arrow concerns the dynamics, admissible states, observations, or boundary conditions.

The recoverable content consists of the following qualitative questions:

1. Is the hypothesis of an intrinsic arrow of time compatible with the successful theoretical treatment of time as a group?
2. Are there uncertainties in the theoretical description of the past, and how do they manifest themselves?
3. How much information about properties of states is lost over time as a consequence of those uncertainties or ambiguities?

No domains, quantitative bounds, or quantifiers over mathematical models can be supplied from this record. In particular, the third question does not specify what information is available initially, which properties are considered, how information is measured, or which time intervals are under consideration.

Qualification on the intended target. The registry labels the record open, but also assigns statement_status: unrecoverable. Its supplied statement-verification note says that the official report presents proposed answers and proved propositions for these expository questions, so the extraction is not a standalone open problem. Accordingly, the questions above preserve the supplied wording without asserting that they constitute a precise unresolved conjecture. Recovering a mathematical statement requires identifying the relevant definitions, hypotheses, propositions, and remaining question in the report.

Short English statement

The record asks whether an intrinsic direction of time can coexist with a group description of time, whether descriptions of the past involve uncertainty, and how that uncertainty causes information loss about states. The mathematical model and measures are unspecified. The supplied verification note identifies these as expository questions with proposed answers and proved propositions, so a standalone open conjecture cannot be recovered from the supplied evidence.

Sources

• Local UnsolvedMath registry, supplied complete record: permanent ID $30005724$, title Information Loss and an Intrinsic Arrow of Time, exact source problem code catalogue entry, collection Oberwolfach Reports Open Problems. No individual proposer is supplied; the proposed year is recorded as 2023.
• Supplied report attribution: Mini-Workshop: Standard Subspaces in Quantum Field Theory and Representation Theory (2024), Oberwolfach Reports, pp. 2851--2901, DOI 10.4171/owr/2023/50. https://doi.org/10.4171/owr/2023/50. The extracted text ends with the report title and page number 2871. The supplied citation year is 2024, while the proposed year and year tag are 2023; this dating distinction has not been resolved.
• Supplied literature source: Arrow of Time and Quantum Physics. https://doi.org/10.1007/s10701-023-00728-4. No authors or precise theorem references are supplied.
• Supplied literature source labelled "original Oberwolfach report": https://doi.org/10.4171/owr/2023/50.
• Literature assessment dated exactly 2026-08-22: the supplied curation labels the status open and states that the arrow-of-time paper develops a model relating causal asymmetry to information loss, while the broad compatibility and uncertainty questions are not settled as general theorems. This is supplied dated curation derived from the OWR record, not an independently verified literature assessment; time-sensitive status and cited claims require independent verification.
• Supplied statement-verification qualification: the official report is said to present proposed answers and proved propositions for these expository questions, and the extraction is said not to be a standalone open problem. This report-specific qualification is retained alongside the supplied open label; neither claim has been independently checked here.