Thermophysics-Informed Phenomenological Framework for Molten Material Self-Organization in Laser Remelting-Based Surface Polishing: Conceptualization and Preliminary Analysis

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. This study defines laser polishing as an open and non-equilibrium self-organization system and uses the Lyapunov exponent, approximate entropy, and Hurst exponent to characterize its chaotic properties. However, it does not establish a quantitative relationship between these chaos metrics and intrinsic thermophysical parameters (e.g., temperature gradient, cooling rate, surface tension gradient, Marangoni number). How can you ensure the physical meaning of chaos metrics is strictly consistent with the actual thermophysical processes?
2. Experiments are limited to a single scanning speed (20 mm/s), a narrow range of laser fluence (131.4–184.3 mJ/cm²), and only Inconel 718 alloy. The evolution and universality of chaotic characteristics under shallow and deep laser polishing regimes are not validated. Can this phenomenological framework be generalized to other metallic materials or wider processing windows.
3. The study claims that contracted phase portrait, reduced entropy, and increased Hurst exponent correspond to improved surface quality. Nevertheless, laser remelting involves multiple nonlinear factors such as melt flow, interface instability, and solidification undercooling. How do you separate and quantify the contributions of “self-organized smoothing” and “thermodynamic instability” to the final topography, to avoid coupling interference with chaos indicators?

Author Response

General Comment to Associate Editor and Reviewer #1

 

The author would like to thank the Associate Editor and Reviewer #1 for the constructive evaluation of the manuscript. The reviewer’s general assessment indicates that the manuscript is sound in terms of language quality, research design, and presentation, while certain aspects of methodology, results, and conclusions could be further improved.

 

In response, the author has carefully considered all comments. Where appropriate, clarifications have been incorporated to improve the presentation and interpretation of the work. At the same time, several comments relate to extensions of the study beyond its intended scope (e.g., full thermophysical coupling, broad parametric generalization, and decomposition of coupled nonlinear mechanisms). These aspects have been addressed conceptually in the responses, while maintaining the original focus of the manuscript on a thermophysics-informed phenomenological framework.

 

Reviewer: 1

 

The author would like to express sincere thanks to the anonymous reviewer for the insightful comments.

 

General Marks and Comments:

Quality of English Language:

(x) The English is fine and does not require any improvement.

	Yes	Can be improved	Must be improved	Not applicable
Does the introduction provide sufficient background and include all relevant references?	(x)	( )	( )	( )
Is the research design appropriate?	(x)	( )	( )	( )
Are the methods adequately described?	( )	(x)	( )	( )
Are the results clearly presented?	( )	(x)	( )	( )
Are the conclusions supported by the results?	( )	(x)	( )	( )
Are all figures and tables clear and well-presented?	(x)	( )	( )	( )

 

Response to Reviewer #1 – General Remarks:

 

The author would like to sincerely thank the reviewer for the positive evaluation of the manuscript. The reviewer’s assessment that the English language is clear, the introduction provides sufficient background, the research design is appropriate, and the figures and tables are well presented is greatly appreciated. The reviewer’s assessment that the English language is clear, the introduction provides sufficient background, the research design is appropriate, and the figures and tables are well presented is greatly appreciated.

 

The indication that certain aspects (methods, results, and conclusions) can be further improved has been carefully considered. Clarifications have been made where necessary to enhance the presentation and interpretation of the results. For comments suggesting broader quantitative modeling, extended parametric studies, or decomposition of coupled thermophysical effects, the author respectfully notes that these directions extend beyond the scope of the present work. These points have been addressed conceptually while preserving the intended focus of the manuscript.

 

C1.1.    This study defines laser polishing as an open and non-equilibrium self-organization system and uses the Lyapunov exponent, approximate entropy, and Hurst exponent to characterize its chaotic properties. However, it does not establish a quantitative relationship between these chaos metrics and intrinsic thermophysical parameters (e.g., temperature gradient, cooling rate, surface tension gradient, Marangoni number). How can you ensure the physical meaning of chaos metrics is strictly consistent with the actual thermophysical processes?

 

A1.1.   The author appreciates the reviewer’s comment; however, it is important to clarify the intended scope and contribution of the present work.

 

The establishment of a direct quantitative relationship between chaos-based descriptors (e.g., Lyapunov exponent, approximate entropy, Hurst exponent) and intrinsic thermophysical parameters such as temperature gradients, cooling rates, or Marangoni numbers would require a fully coupled thermophysical modeling framework, combining high-fidelity numerical simulations (e.g., CFD with phase change and thermocapillary flow) with synchronized experimental validation. Such an undertaking represents a significantly broader and fundamentally different research objective, which is beyond the scope of the present study.

 

The primary contribution of this work is the development of a thermophysics-informed phenomenological framework, in which the measured surface topography is interpreted as a spatially resolved, integrated manifestation of melt-pool dynamics. Within this framework, chaos-based metrics are not intended to serve as direct proxies for individual thermophysical parameters. Instead, they function as reduced-order descriptors of system behavior, capturing sensitivity, regularity, and persistence of the underlying nonlinear processes. The physical relevance of these descriptors is ensured through their consistent interpretation in the context of established thermophysical mechanisms governing laser polishing, including transient heat conduction, thermocapillary (Marangoni) convection, capillary-driven flow, and rapid solidification. This interpretation has been explicitly discussed in the manuscript (Section 2.2).

 

It should be emphasized that the objective of the present study is to establish a conceptual and analytical foundation for linking measurable surface characteristics with process stability, rather than to derive a closed-form or fully calibrated mapping to fundamental thermophysical parameters. The development of such quantitative relationships is acknowledged as an important direction for future work, particularly in the context of integrating this framework with physics-based simulations and digital twin approaches. We have addressed the comment conceptually and no further changes are considered necessary within the scope of the present work.

 

C1.2.   Experiments are limited to a single scanning speed (20 mm/s), a narrow range of laser fluence (131.4–184.3 mJ/cm²), and only Inconel 718 alloy. The evolution and universality of chaotic characteristics under shallow and deep laser polishing regimes are not validated. Can this phenomenological framework be generalized to other metallic materials or wider processing windows.

 

A1.2.   The author thanks the reviewer for this important comment and would like to clarify the scope and intent of the experimental design.

 

The experimental conditions in this study were intentionally restricted to a single scanning speed and a narrow range of laser fluence in order to ensure a well-controlled environment for isolating the fundamental thermophysical mechanisms governing melt-pool dynamics and surface evolution. As stated in the manuscript, the objective of this work is not to provide a comprehensive parametric study or to experimentally validate all processing regimes (e.g., shallow versus deep laser polishing), but rather to develop and demonstrate a thermophysics-informed phenomenological framework for analyzing molten material self-organization.

 

Within this context, the use of a single material (Inconel 718) and a limited parameter window allows for a clear and unambiguous interpretation of the relationship between process conditions, melt-pool behavior, and the resulting chaos-based descriptors, without the confounding effects of a high-dimensional parameter space. This approach is consistent with first-stage, hypothesis-driven investigations, where establishing physically meaningful relationships takes precedence over broad empirical generalization.

 

Regarding generalization, the proposed framework is not inherently material-specific, as it is grounded in fundamental thermophysical processes common to metallic systems undergoing laser remelting, including transient heat conduction, thermocapillary (Marangoni) convection, capillary-driven flow, and rapid solidification. The chaos-based descriptors are applied to the resulting surface topographies, which represent integrated manifestations of these underlying processes, and are therefore expected to retain their interpretative relevance across different materials and processing conditions.

 

However, it is acknowledged that the quantitative behavior and sensitivity of these descriptors may vary depending on material properties and processing regimes. The validation of the framework across a wider range of materials, scanning speeds, and laser fluences—including explicit differentiation between shallow and deep polishing regimes—is an important direction for future work and will be addressed in subsequent studies.

 

This aspect is already addressed conceptually in the manuscript within the defined scope of the study. Therefore, no additional modifications are necessary.

 

C1.3.   The study claims that contracted phase portrait, reduced entropy, and increased Hurst exponent correspond to improved surface quality. Nevertheless, laser remelting involves multiple nonlinear factors such as melt flow, interface instability, and solidification undercooling. How do you separate and quantify the contributions of “self-organized smoothing” and “thermodynamic instability” to the final topography, to avoid coupling interference with chaos indicators?

 

A1.3.   The author thanks the reviewer for this thoughtful comment and would like to clarify the methodological position of the present study.

 

It is fully acknowledged that laser remelting is governed by multiple strongly coupled and nonlinear thermophysical phenomena, including melt flow, interface instability, thermocapillary convection, and rapid solidification under nonequilibrium conditions. In such systems, the separation and independent quantification of individual contributions—such as “self-organized smoothing” and “thermodynamic instability”—is inherently challenging and, in general, requires high-fidelity multiphysics modeling and controlled perturbation analysis, which are beyond the scope of the present work.

 

The framework proposed in this study does not aim to decompose the final surface topography into independently quantifiable contributions of competing mechanisms. Instead, it is based on the premise that the measured surface topography represents a cumulative and integrated outcome of all underlying thermophysical processes occurring within the melt pool. Within this context, the applied chaos-based descriptors (phase portrait characteristics, approximate entropy, and Hurst exponent) are used as holistic indicators of system behavior, capturing the overall degree of organization, stability, and persistence of the process dynamics.

 

Accordingly, the observed relationships—such as contraction of the phase portrait, reduction in entropy, and increase in the Hurst exponent—are interpreted as system-level signatures of more stable and coherent melt-pool dynamics, which manifest as improved surface quality. These descriptors are not intended to isolate or quantify the individual contributions of specific physical mechanisms, but rather to reflect their combined effect on the evolution of surface topography.

 

This aspect is consistent with the thermophysics-informed phenomenological nature of the proposed framework, where the emphasis is placed on identifying measurable indicators of process stability rather than performing a full mechanistic decomposition of coupled nonlinear effects.

 

This aspect is already addressed in the manuscript at the conceptual level, consistent with the scope of the work, through the interpretation of surface topography as an integrated manifestation of melt-pool dynamics. Therefore, no further revisions are warranted within the scope of the present study.

 

Reviewer 2 Report

Comments and Suggestions for Authors

The main value of the work is the departure from purely empirical trial-and-error optimization and currently popular methods based on neural networks in favour of a phenomenological framework based on nonlinear dynamic.

This is preliminary research, so groundbreaking results could not be expected. Nevertheless, the work is valuable and should be published after some corrections, which are listed below.

===

Unfortunately, Figure 3, which is crucial for understanding the overall work, is not clearly legible due to the lack of a sufficient and clear captions. For example, it is unclear what is shown in Figure 3b or even whether its axis descriptions are correct.

Some of the descriptions of the elements of Figure 3 are scattered throughout the text, but all of them should be included below the figure. If necessary, Figure 3 can be divided into two parts for clarity.

The same remarks are valid for Figure 4.

===

Table presents data for five different fluences (131.4, 143.9, 158.3, 166.3, 184.3 mJ/cm2) while the text in Section 3 only mentions performing experiments with three fluences (131.4, 158.3, and 184.3 mJ/cm2). The text provides no explanation for where the additional data points (143.9 and 166.3) came from or how they were derived.

===

In Section 4.1, the text:

"the lowest Lyapunov exponent of 1.955 for all hLP(x) profiles corresponds to the optimal surface quality (obtained at 158.3 mJ/cm2)." (p.9, l. 350)

If you examine Table 1 (p. 9), the Lyapunov exponents for the hLP(x) profiles are listed as: 2.177, 2.121, 2.242, 2.239, and 2.468. None of these values equal 1.955. The value 1.955 does not appear anywhere in the data table.

===

The work conflates the concepts of thermodynamic entropy and information entropy. Surface roughness is a geometric state, not a thermodynamic state function. The process of reducing surface roughness dissipates energy as heat, which actually increases the entropy of the universe. The paper’s naming of "low-entropy regimes" is perhaps metaphorically descriptive but physically inaccurate.

In my opinion, confusion should be avoided.

===

The author assumes the surface topography is an accurate map of the fluid dynamics, ignoring the high-speed solidification front which may freeze in features that are not representative of the chaotic flow itself. The metrics are calculated post-factum from the resulting surface. While these metrics correlate with roughness, they do not prove that the melt pool behaved according to these chaos parameters. For instance the Hurst exponent measuring "persistence" is a description of the result (the topography), not a measurement of the process (the fluid dynamics)

Real-world flow behaviour studies require real-time recording during the process. Of course, for utilitarian purposes, such measurements are unnecessary, but confusion should be avoided in the analysis.

===

In Section 3, we see that the initial and laser-polished surfaces exhibit strong cross-correlation. However, if the profiles are 98% correlated, the laser polishing process does not significantly alter the surface structure. Therefore, polishing merely smooths the surface (spatial low-pass filter) while preserving the underlying geometry. If the process truly "redistributes the melt" to "fill the peaks and fill the valleys," one would expect a significant decrease in the correlation between the initial and final profiles. The author uses the high correlation to justify his sampling method, but this same high correlation undermines the claim that the process significantly "self-organizes" the melt.

===

The Conclusions section does not contain any significant conclusions, it can and must be improved. For example (in random order):

-- The Hurst Exponent appears to be a legitimate proxy for surface state. The Hurst exponent was the only metric that showed a consistent, well-defined pattern across the laser-material interaction zone (the melt pool). If an engineer wants to implement an in-line quality control system, the Hurst exponent of the surface profile could serve as a useful metric to determine if the process is "persistent" (stable/smooth) or "stochastic" (unstable/rough). It may be a more robust indicator of surface state than simple Ra or Rq parameters, which may be too noisy for real-time control.

-- The data demonstrates that LP acts as a spatial low-pass filter. The study shows a significant reduction in the amplitude of the 20 mm⁻¹ spatial frequency component (the frequency dictated by the initial micromilling step-over). This confirms that laser polishing can be effective at removing the periodic patterns left by traditional milling. For an engineer, this validates that LP can be used as a step specifically to remove tool marks, provided the laser parameters are correctly tuned to the spatial frequency of the previous machining operation.

-- The study confirms that molten material exhibits a directional bias. New peaks in the polished profile shift in the direction opposite to the laser-scanning velocity. This is a crucial observation for tool-path planning, especially when polishing a complex geometry.

-- The optimal fluence for given material (Inconel 718) and LP parameters is 158.3 mJ/cm², Ra improved by 70%

 

 

Author Response

General Comment to Associate Editor and Reviewer #2

 

The author would like to thank the Associate Editor and Reviewer #2 for the constructive evaluation of the manuscript. The reviewer’s general assessment indicates that the manuscript is sound in terms of language quality, research design, and presentation, while certain aspects of methodology, results, and conclusions could be further improved.

 

The author would like to express sincere thanks to the anonymous reviewer for the insightful comments.

 

Reviewer: 2

 

General Marks and Comments:

Quality of English Language:

(x) The English is fine and does not require any improvement.

	Yes	Can be improved	Must be improved	Not applicable
Does the introduction provide sufficient background and include all relevant references?	(x)	( )	( )	( )
Is the research design appropriate?	(x)	( )	( )	( )
Are the methods adequately described?	(x)	( )	( )	( )
Are the results clearly presented?	( )	( )	(x)	( )
Are the conclusions supported by the results?	( )	(x)	( )	( )
Are all figures and tables clear and well-presented?	( )	( )	(x)	( )

 

The main value of the work is the departure from purely empirical trial-and-error optimization and currently popular methods based on neural networks in favour of a phenomenological framework based on nonlinear dynamic. This is preliminary research, so groundbreaking results could not be expected. Nevertheless, the work is valuable and should be published after some corrections, which are listed below.

 

Response to Reviewer #2 – General Remarks:

 

The author would like to sincerely thank Reviewer #2 for the thoughtful and constructive evaluation of the manuscript. The reviewer’s recognition of the main value of the work—namely, the departure from purely empirical trial-and-error optimization and currently popular neural-network-based approaches toward a phenomenological framework grounded in nonlinear dynamics—is greatly appreciated.

 

The author also appreciates the reviewer’s balanced assessment that this is preliminary research, where groundbreaking results should not necessarily be expected, while still recognizing that the study provides a valuable contribution worthy of publication after revision.

 

Particular attention has been given to the reviewer’s indication that the presentation of results and the clarity of figures/tables require improvement. These aspects have been carefully considered and revised accordingly.

 

The author is grateful for the recommendation for publication subject to corrections, and a detailed point-by-point response is provided below.

 

C2.1. Unfortunately, Figure 3, which is crucial for understanding the overall work, is not clearly legible due to the lack of a sufficient and clear captions. For example, it is unclear what is shown in Figure 3b or even whether its axis descriptions are correct. Some of the descriptions of the elements of Figure 3 are scattered throughout the text, but all of them should be included below the figure. If necessary, Figure 3 can be divided into two parts for clarity. The same remarks are valid for Figure 4.

 

A2.1. The author would like to thank the reviewer for this important and constructive comment and fully agrees that the clarity of Figures 3 and 4, particularly in terms of caption completeness, must be improved.

 

In response, the captions of Figures 3 and 4 have been revised and expanded to provide a clear, self-contained description of all sub-figures, including explicit identification of the data presented (e.g., surface topographies, central profiles, and corresponding statistical characteristics), as well as clarification of axes and notation. These revisions have been incorporated on page 8 of the manuscript, ensuring that the figures can be interpreted independently without requiring extensive cross-referencing to the main text.

 

With respect to the suggestion to divide Figures 3 and 4 into multiple parts, the author respectfully believes that such modification is not advisable. These figures are intentionally structured to present a comprehensive and integrated view of the experimental results, combining measured surface topographies, extracted profiles, and derived statistical descriptors within a unified framework. Separating these elements into multiple figures would disrupt the direct visual correspondence between experimental observations and their analytical interpretation, thereby reducing clarity rather than improving it.

 

In addition, the author would like to note that the final placement and layout of Figures 3 and 4 in the manuscript are subject to the publisher’s formatting requirements, and their exact positioning will be determined during the production stage.

 

Therefore, the figures have been retained in their original structure, while their readability and interpretability have been significantly enhanced through improved captions and clearer descriptions.

 

C2.2.   Table presents data for five different fluences (131.4, 143.9, 158.3, 166.3, 184.3 mJ/cm2) while the text in Section 3 only mentions performing experiments with three fluences (131.4, 158.3, and 184.3 mJ/cm2). The text provides no explanation for where the additional data points (143.9 and 166.3) came from or how they were derived.

 

A2.2. The author would like to thank the reviewer for the careful reading of the manuscript and for this very valuable observation. The reviewer is correct that an inconsistency exists between the description in Section 3 and the data presented in the table. This was due to an oversight in the manuscript text. In fact, all five laser fluences (131.4, 143.9, 158.3, 166.3, and 184.3 mJ/cm²) were used in the experiments and should have been consistently reported. This has been corrected on page 7 of the revised manuscript, where the full set of experimental conditions is now clearly stated.

 

C2.3.   In Section 4.1, the text: "the lowest Lyapunov exponent of 1.955 for all hLP(x) profiles corresponds to the optimal surface quality (obtained at 158.3 mJ/cm2)." (p.9, l. 350) If you examine Table 1 (p. 9), the Lyapunov exponents for the hLP(x) profiles are listed as: 2.177, 2.121, 2.242, 2.239, and 2.468. None of these values equal 1.955. The value 1.955 does not appear anywhere in the data table.

 

A2.3.   The author would like to thank the reviewer for the careful and detailed examination of the manuscript and for identifying this inconsistency. The reviewer is correct that the reported value of 1.955 does not correspond to the data presented in Table 1. This was an error in the manuscript. The table and corresponding values have been carefully rechecked and corrected for consistency. In addition, the wording “optimal surface quality” has been revised to “best-achieved surface quality” to more accurately reflect the scope and intent of the study. It is emphasized that this inconsistency was editorial in nature and does not affect the underlying analysis, interpretation, or conclusions of the work. These corrections have been implemented in the revised manuscript.

 

C2.4.   The work conflates the concepts of thermodynamic entropy and information entropy. Surface roughness is a geometric state, not a thermodynamic state function. The process of reducing surface roughness dissipates energy as heat, which actually increases the entropy of the universe. The paper’s naming of "low-entropy regimes" is perhaps metaphorically descriptive but physically inaccurate. In my opinion, confusion should be avoided.

 

A2.4.   The author would like to thank the reviewer for this important and insightful comment regarding the distinction between thermodynamic entropy and information entropy. The reviewer is correct that surface roughness is not a thermodynamic state function, and that, from a strict thermodynamic perspective, the overall entropy of the system and its surroundings increases due to energy dissipation during laser remelting. The use of the term “low-entropy regime” in the manuscript is therefore not intended to imply a direct equivalence with thermodynamic entropy in the classical sense.

 

In the present work, entropy is evaluated in the sense of information entropy, derived from the statistical structure of surface topography. Within the proposed framework, this measure is used as a descriptor of the degree of spatial order and regularity in the resulting surface, rather than as a direct thermodynamic quantity. It is further noted that thermodynamic entropy associated with such highly localized, transient, and nonequilibrium processes cannot be directly measured experimentally. In this context, the proposed approach provides a pathway for indirectly assessing the outcome of thermodynamically governed processes through measurable surface characteristics. Specifically, the surface topography is interpreted as an integrated result of the underlying thermophysical dynamics, and the corresponding information entropy is used as a phenomenological, reduced-order indicator reflecting the degree of organization emerging from these processes, rather than a direct measure of thermodynamic entropy itself.

 

The underlying assumption of the framework is that more stable melt-pool dynamics tend to produce more regular and predictable surface topographies, which are characterized by lower information entropy. In this sense, information entropy serves as a phenomenological proxy for process stability, rather than a thermodynamic state variable. To avoid potential confusion, the manuscript has been revised (see page 5) to explicitly clarify this distinction and to ensure that entropy-related terminology is used in a phenomenological and descriptive context.

 

C2.5.   The author assumes the surface topography is an accurate map of the fluid dynamics, ignoring the high-speed solidification front which may freeze in features that are not representative of the chaotic flow itself. The metrics are calculated post-factum from the resulting surface. While these metrics correlate with roughness, they do not prove that the melt pool behaved according to these chaos parameters. For instance the Hurst exponent measuring "persistence" is a description of the result (the topography), not a measurement of the process (the fluid dynamics). Real-world flow behaviour studies require real-time recording during the process. Of course, for utilitarian purposes, such measurements are unnecessary, but confusion should be avoided in the analysis.

 

A2.5.   The author would like to thank the reviewer for this insightful and technically important comment. The reviewer is correct in noting that the surface topography represents a post-process outcome, and that rapid solidification may preserve features that do not directly correspond to instantaneous melt-pool flow structures. In this sense, the measured topography cannot be interpreted as a direct or complete map of the underlying fluid dynamics during laser remelting.

 

The present study does not assume a one-to-one correspondence between instantaneous melt-pool behavior and the resulting surface features. Instead, the adopted approach is based on the premise that the final surface topography constitutes an integrated and physically constrained outcome of the coupled thermophysical processes, including melt flow, heat transfer, and rapid solidification. As such, it provides a measurable representation of the cumulative effect of process dynamics, rather than a direct observation of them.

 

Accordingly, the applied chaos-based metrics (e.g., approximate entropy, Lyapunov exponent, and Hurst exponent) are evaluated from the resulting surface profiles and are interpreted as descriptors of the structural organization and statistical properties of the final state, rather than as direct measurements of melt-pool dynamics. In particular, as correctly noted by the reviewer, the Hurst exponent characterizes persistence in the spatial data series of the surface topography, and is therefore a property of the resulting structure, not a direct measurement of the flow field.

 

The objective of the present work is to establish a phenomenological and practically applicable framework that links measurable surface characteristics with process stability and surface quality. This approach is especially relevant from an engineering perspective, where the final surface topography represents the functional outcome of the process.

 

The author fully agrees that direct investigation of melt-pool dynamics requires real-time diagnostic techniques, such as high-speed thermography or in situ monitoring, which can provide complementary insights into transient flow behavior. The proposed framework is therefore not intended to replace such methods, but rather to provide a post-process analytical perspective that can be used independently or in conjunction with real-time measurements.

 

To avoid potential ambiguity, the manuscript has been revised to clarify that the presented analysis is based on post-process characterization of surface topography, and that the derived metrics describe the resulting structure rather than directly measuring the underlying fluid dynamics.

 

C2.6.   In Section 3, we see that the initial and laser-polished surfaces exhibit strong cross-correlation. However, if the profiles are 98% correlated, the laser polishing process does not significantly alter the surface structure. Therefore, polishing merely smooths the surface (spatial low-pass filter) while preserving the underlying geometry. If the process truly "redistributes the melt" to "fill the peaks and fill the valleys," one would expect a significant decrease in the correlation between the initial and final profiles. The author uses the high correlation to justify his sampling method, but this same high correlation undermines the claim that the process significantly "self-organizes" the melt.

 

A2.6.   The author would like to thank the reviewer for this thoughtful comment and for carefully examining the interpretation of correlation in the manuscript. It appears that the concern arises from a misinterpretation of the profiles presented in Section 3, which describes the methodology for analyzing self-organization, rather than the analysis results themselves.

 

In the figure referenced in this section, three profiles are presented: the initial profile h_ini(x), the laser-polished profile h_LP(x), and their difference Δh(x) = h_LP(x) − h_ini(x). The profile that may appear similar to the initial profile corresponds to the difference profile Δh(x), not the remelted profile. Due to the definition of Δh(x), and the tendency of the remelted profile toward a smoother (near-flat) shape, the difference profile can visually resemble the initial profile, which may lead to the impression of high correlation.

 

The visually perceived high correlation (≈98%) refers to the consistency of initial surface profiles within the micromilled region, and is used to justify the sampling methodology. It does not imply that the remelted profile remains highly correlated with the initial one, nor does it contradict the observed smoothing and redistribution effects of the laser polishing process. Furthermore, Section 3 is intended to illustrate the analysis framework, rather than to present the full extent of topography transformation, which is analyzed quantitatively in Section 4.

 

This aspect is appropriately represented in the manuscript, and the comment has been addressed through clarification of its interpretation.

 

C2.7a. The Conclusions section does not contain any significant conclusions, it can and must be improved. For example (in random order):

-- The Hurst Exponent appears to be a legitimate proxy for surface state. The Hurst exponent was the only metric that showed a consistent, well-defined pattern across the laser-material interaction zone (the melt pool). If an engineer wants to implement an in-line quality control system, the Hurst exponent of the surface profile could serve as a useful metric to determine if the process is "persistent" (stable/smooth) or "stochastic" (unstable/rough). It may be a more robust indicator of surface state than simple Ra or Rq parameters, which may be too noisy for real-time control.

C2.7b. The data demonstrates that LP acts as a spatial low-pass filter. The study shows a significant reduction in the amplitude of the 20 mm⁻¹ spatial frequency component (the frequency dictated by the initial micromilling step-over). This confirms that laser polishing can be effective at removing the periodic patterns left by traditional milling. For an engineer, this validates that LP can be used as a step specifically to remove tool marks, provided the laser parameters are correctly tuned to the spatial frequency of the previous machining operation.

C2.7c.  The study confirms that molten material exhibits a directional bias. New peaks in the polished profile shift in the direction opposite to the laser-scanning velocity. This is a crucial observation for tool-path planning, especially when polishing a complex geometry.

C2.7d. The optimal fluence for given material (Inconel 718) and LP parameters is 158.3 mJ/cm², Ra improved by 70%

 

A2.7.   The author would like to thank the reviewer for this comprehensive and constructive set of comments regarding the Conclusions section. The suggestions provided are insightful and helpful in strengthening the clarity and practical relevance of the manuscript.

In response, the Summary and Conclusions section has been completely rewritten to more clearly articulate the key findings of the study and to better reflect both the phenomenological framework and the experimentally observed trends.

 

In particular, the revised Conclusions now explicitly emphasize that:

• laser polishing acts as a spatial low-pass filter, effectively attenuating high-frequency surface components associated with micromilling marks;
• the process exhibits a directional bias in material redistribution, with surface features shifting relative to the laser scanning direction;
• the Hurst exponent demonstrates consistent behavior across the investigated conditions and can serve as a robust descriptor of surface state in post-process analysis;
• a laser fluence of 158.3 mJ/cm² provided the best-achieved surface quality, corresponding to approximately 70% improvement in Ra within the studied parameter range (rather than implying a globally optimal condition).

 

At the same time, the author would like to clarify that surface topography-based descriptors, including the Hurst exponent, are derived from post-process measurements and therefore are not directly applicable for in-line process control. Their role is in post-process characterization and interpretation of process outcomes. In addition, conventional roughness parameters such as Ra and Rq are not inherently “noisy,” but rather represent statistical measures of surface variability, reflecting the stochastic nature of the process.

 

Overall, the revised Conclusions section now provides a more balanced presentation of both the scientific contribution (thermophysics-informed phenomenological framework) and the practical implications of the findings, while maintaining consistency with the scope and limitations of the study.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

All reviewer comments have been fully addressed, and the manuscript has been significantly improved. The article can be published in its current form.