In this article
- Which operation carries the bound
- What the SMM/DTT distinction contributes
- A numerical benchmark with units
- The DTT memory cycle
- What would count as a new result
- A further conceptual benchmark
Time and information: SMM/DTT and Landauer’s principle
A physical theory of temporal records must account for the memory that carries them. Landauer’s principle constrains a particular operation—erasure under stated conditions—rather than assigning a universal energy price to every tick. A worked numerical example shows how SMM/DTT can incorporate information thermodynamics without confusing record creation, copying and reset.
01Which operation carries the bound
Consider a memory bit whose two logical states are initially equally likely and energetically equivalent. Resetting it to one standard state reduces its logical entropy. In an ideal isothermal process with an appropriate reservoir, the familiar minimum heat delivered to the environment is kBT ln 2. The initial distribution, available side information and physical implementation matter. This is not a universal claim that every computation or observation must dissipate exactly that amount. [1]
02What the SMM/DTT distinction contributes
SMM begins with one nonspatial generative source. DTT distinguishes its inner production from the outer order in which completed results become accessible. The six inner levels are nested functional dependencies within that production; the seventh denotes outer completion. They are not six independent clocks, six spatial directions, or six simultaneously occupied temporal axes. This distinction makes the framework more specific than a general claim that everything changes: it asks how a world of persistent relations can be generated before its spatial representation is taken for granted.
An arrow of time is an asymmetry with a specified meaning. A causal arrow concerns permitted influence; a thermodynamic arrow concerns typical entropy change; a psychological arrow concerns memory and anticipation. SMM/DTT adds a proposed generative orientation: production is organized toward completion, after which a result can participate in later records. These orientations can support one another, but their agreement is an explanatory question. A growing archive by itself says nothing about the entropy of the entire universe, and a time-symmetric microscopic law can still support asymmetric records when supplied with asymmetric conditions.
The phrase dual arrows is most useful when it names the relation between inner completion and outer succession. The inner orientation is functional: unfinished and finished configurations have different roles. The outer orientation is historical: a retained result can constrain later access. They need not be opposite vectors drawn on a plane. Drawing two arrows can obscure the real issue if no criterion identifies what reverses when an arrow is reversed. For example, reversing a movie reverses the displayed order, whereas unmaking its records would also require reversing changes in the storage device and environment. [2]
03A numerical benchmark with units
At T = 300 K, using kB = 1.380649 × 10⁻²³ J/K, the bound is approximately 2.871 × 10⁻²¹ joules per unbiased erased bit. Erasing one billion such bits corresponds to approximately 2.871 × 10⁻¹² joules at the ideal bound. Actual devices can dissipate much more. The temperature cancels the inverse-kelvin unit of kB, leaving energy. This does not determine the mass or frequency of a fundamental source; it constrains a specified memory operation in a specified thermal setting.
Qmin = kBT ln 2 ≈ 2.871 × 10⁻²¹ J at 300 K
04The DTT memory cycle
Inner generation can create correlations, outer completion can make a selected record available, and later reuse of a finite memory may require reset. These are distinct stages of a resource account. A reversible copy into a prepared blank register need not be identified with erasure. A source model repeatedly assuming fresh blank memory should explain where that resource comes from. The six nested levels do not eliminate this obligation: nesting organizes operations, while thermodynamics constrains their implementation. A complete cycle includes memory, source, environment and correlations used as resources.
05What would count as a new result
SMM/DTT could derive a lower bound on a particular completion protocol’s memory or heat cost, or show that a proposed record rate is incompatible with its resource budget. Such a result would constrain the programme from within. It would not follow merely by multiplying a universal tick count by kBT ln 2. The relevant bits must be independently identified and the erased uncertainty calculated. This comparison turns information into a precise physical resource while preserving the philosophical question of why temporal continuity depends on retained relations.
06A further conceptual benchmark
Take a memory initially in a known state 0 and a fair bit X. A reversible copy maps (X,0) to (X,X). Before copying, the two devices are uncorrelated; afterwards they share one bit of mutual information. No information has been erased in this ideal operation. The record points toward the earlier value because of the initially blank memory and the chosen interaction. Restoring only the memory to 0 is a different operation, with a thermodynamic cost under the usual erasure assumptions. This simple distinction shows how a record arrow can depend on preparation without proving a fundamental violation of time-reversal symmetry. It also shows why a source-memory budget belongs inside any physical completion model.
THE SAME QUESTION, DIFFERENT STARTING POINTS
The comparison at a glance
| Question | SMM/DTT | Landauer’s principle |
|---|---|---|
| Information retention | DTT’s completed records require a stated distinction between information retained, transferred and overwritten. | Landauer’s principle constrains specified logically irreversible reset tasks under physical thermodynamic assumptions. |
| Resource calculation | A source-memory budget must identify which uncertainty is actually erased before assigning a heat cost. | At 300 K, ideal unbiased-bit erasure has the benchmark kBT ln 2 ≈ 2.87 × 10⁻²¹ joules. |
KEEP THE CONNECTION
Key ideas
- Consider a memory bit whose two logical states are initially equally likely and energetically equivalent.
- SMM/DTT could derive a lower bound on a particular completion protocol’s memory or heat cost, or show that a proposed record rate is incompatible with its resource budget.
- A source-memory budget must identify which uncertainty is actually erased before assigning a heat cost.
Continue on SMONAD
- Renewal and persistence: why a changing world can keep a history →
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- The 'Chest' of Time →
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- Time Chest →
Connects this comparison with the author’s discussion of identity.
Sources and further reading
References support the comparator and the specific mathematical or interpretive claims indicated. SMM/DTT connections are developed in the analysis above.
- R. Landauer, Irreversibility and Heat Generation in the Computing Process (1961) ↗Original thermodynamics of logically irreversible computation; used with stated equilibrium and memory assumptions.
- Mohamed Haj Yousef, The duality-of-time postulate, SMONAD ↗Author’s presentation of SMM/DTT; source ontology and nested inner generation distinguished from outer completion.
How these comparisons distinguish premises, results and physical claims