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Beyond the arrow of time: can there be a relation between measurement of entropy and time?
1  Department of Mechanical and Aerospace Engineering, Syracuse University


The tendency of the entropy of isolated to increase is considered to be directly linked to the direction of the flow of time. This raises the question whether a quantitative relation can be established such that a time interval can be measured by measuring entropy change and vice versa. The existence or absence of such a link also calls for further consideration of the nature of time. Prigogine argued that the true nature of time can only be discovered by investigating this phenomenon using scientific and philosophical methods. If this is true, then ongoing debates in the metaphysics of time and progress in the scientific study of entropy can be brought together to shed light on this fascinating but elusive concept. In this paper, starting from my recent modified definition of entropy change as a non-dimensional measure of energy change, a direct link between entropy and time duration is presented. It draws from steady energy transfer processes such as heat transfer and shows that a measure of time can be found to be associated with a measure of entropy change. In the absence of other driving forces, the passage of time in an isolated system can therefore be tracked with a well calibrated entropy change meter. When other forces are allowed to interfere and there is no external point from which the system can be considered to be isolated, then the measure of time is non-monotonous since an isolated system can be restored to an earlier state of non-equilibrium.

Keywords: arrow of time, entropy increase principle, heat transfer, non-equilibrium isolated systems
Comments on this paper
Anna Birzina
Entropic Measure of Time
The idea of interrelation between time and entropy (the introduction of a measure of time through entropy) is not new. Review and development of this idea can be found in the articles (L. M. Martyushev, E. V. Shaiapin. Entropic Measure of Time, and Gas Expansion in Vacuum// Entropy (2016)18(6), 233; L. M. Martyushev. On Interrelation of Time and Entropy// Entropy (2017) 19 345). It is a pity that the author did not know about it and does not refer to these works. We very much want to hope that future publications of author will take this remark into account.

Prof. Leonid Martyushev and Dr. Anna Birzina
Ben Akih-Kumgeh
Dear Prof. Martyushev and Dr. Birzina,

Thank you for your critical comment. I sincerely apologize for not carrying out a thorough review of the literature in writing my article. As you can see, I paid greater attention to the discussion of this problem in philosophical literature. But I am also glad to see that others consider this an important problem in the sciences and that we independently reach what may considered to be similar conclusions, though Prof. Martyushev starts out postulating dt as proportional to entropy change.

I will read the two papers more closely and consider extending my paper to recognize this previous work and situate my views in the expanding literature. I note that your approach proceeds from statistical thermodynamics and in the case of the expanding gas, this is akin to a canonical ensemble. The analysis reveals in the end that time evolves as the log of volume. t2-t1 would correspond to the log of ratio of final to initial volume. If these two volumes are close by, then the log can be approximated as t2-t1=(V2-V1)/V1, thus speaking to a linear relation between time change and entropy change for slow expansions and their immediate vicinity. I do observe that your model problem does not completely isolate the problem from the rest of the universe. If the average particle velocity is to remain constant, is this not on account of radiation absorption or heat transfer of some sort? Can't one still carry out average of velocities in a given locality to introduce the concept of temperature as a measure of the microscopic kinetic energy? I think the result you arrive at in your earlier paper concerning the volume change, this can be obtained from the classical thermodynamic expression of entropy change of an ideal gas in which an isothermal process is assumed. The entropy change associated with heat absorption manifests itself as a change in the log of the volume.

Thank you for your comment and once more, my apologies for the incomplete review. I will expand the paper to recognize the priority of your result.

Best regards,

Ben Akih