Soumendra Nath Thakur
April 13, 2025
Entropy and Time (∆t):
Why in entropy, ∆t = Constant:
Because, ∆t = constant is not merely a convenient assumption; it is a foundational necessity for the meaningful evolution of entropy.
In the context of entropy, time is not treated as an independently existing substance or dimension, but rather as an emergent abstraction that measures the rate of existential change. The key requirement is that this measurement must occur on a consistent scale. Thus:
∆t = constant is essential not because time exists on its own, but because a fixed temporal scale is required to interpret and quantify changes in existence consistently.
This principle becomes critically evident in entropy equations:
S = -k² T ln(2) t/h
where entropy S evolves as a linear function of time. This linearity implicitly assumes that each increment of time (∆t) contributes a uniform amount to the evolution of entropy. If ∆t were not constant, the rate of entropy increase would become inconsistent or undefined.
Why ∆t = constant is Required:
If both:
The magnitude of existential change, and the scale or unit of time (∆t) are allowed to vary independently, then:
1. There’s no fixed frame to evaluate how much change is occurring.
2. Entropy loses its predictable progression—undermining not just our calculations, but our very capacity to define "change."
3. This leads to epistemological collapse: without a stable scale, even the concept of evolution or increase becomes meaningless.
Conclusion:
In entropy, ∆t = constant is a scientifically grounded requirement—not a philosophical preference. It ensures that we can observe, define, and quantify change in a coherent way. Without this fixed scale of time, the entire framework of entropy—and by extension, the measurable flow of existence—collapses into ambiguity.
Why the equation S = -k² T ln(2) t/h does not invalidate the idea that ∆t = Constant} (i.e., time has a constant *scale* in entropy):
1. Time Appears Linearly:
In the equation, time (t) is a linear variable, meaning that entropy increases proportionally with time.
This proportionality only works if each time increment ∆t contributes a consistent, quantifiable amount to the increase in entropy.
If (∆t) were variable or inconsistent, the relationship between entropy and time would be nonlinear or chaotic—which this equation does not suggest.
2. What the Equation Says Physically:
Entropy (S) evolves with:
Temperature (T)
Fundamental constants (k, h)
Information units (via ln(2))
Time (t) as a scaling dimension
This structure implies that:
As time increases by equal steps (i.e. ∆t = constant), entropy increases smoothly, predictably, and deterministically.
3. Quantum Units and Scaling:
t/h tells us time is scaled against Planck's constant.
That doesn't mean time intervals shrink or stretch, it means that quantum effects set the baseline resolution of time.
Thus, quantum scaling is fixed, and so is the emergent unit of time (∆t) as applied in entropy dynamics.
4. Negative Sign Does Not Imply Time Variability:
The negative sign in the equation could indicate:
Directionality of entropy (e.g., increase with time forward)
Convention used in specific derivations
It does not imply variable time, nor does it mean entropy reverses or destabilizes.
5. Why This Supports (∆t = constant}:
If ∆t were not constant:
Entropy increments would not match with linear t .
One’d lose the ability to make precise predictions of entropy change over intervals.
The logarithmic relationship to information (via ln(2)) would also break down, since it relies on discrete, countable steps of change in time.
Conclusion:
The equation S = -k² T ln(2) t/h assumes and requires that the scale of time ∆t is constant for entropy to evolve predictably.
Therefore, this equation does not contradict ∆t = constant; rather, it mathematically and physically confirms it.
Reference:
(1a) Thakur, Soumendra Nath (2024). Re-examining Time Dilation through the Lens of Entropy. Qeios. http://doi.org/10.32388/XBUWVD
(1b) Thakur, Soumendra Nath (2024). Re-examining Time Dilation through the Lens of Entropy. ResearchGate. https://www.researchgate.net/publication/378501318_Re-examining_Time_Dilation_through_the_Lens_of_Entropy
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