Geometric-Physical Coordinate Framework of Phenomena-Time in Open Systems with L-Balance Axis Constraint

Shayan Shamohammadi

doi:doi:10.11648/j.sdp.20260101.15

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Geometric-Physical Coordinate Framework of Phenomena-Time in Open Systems with L-Balance Axis Constraint

Shayan Shamohammadi^*

Published in Science Discovery Physics (Volume 1, Issue 1)

Received: 6 January 2026 Accepted: 31 January 2026 Published: 25 February 2026

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Abstract

Mathematical models used in hydrology, physics, chemistry, and many engineering systems are largely based on empirical or semi-empirical relationships. One fundamental reason for this is that classical coordinate systems—whether Cartesian or relativistic spacetime—are inherently incapable of representing the laws of conservation in open systems. These frameworks describe the instantaneous state of quantities, but do not inherently incorporate the flow, input–output balance, and irreversible nature of processes into their geometric structure. In this paper, a new geometric–physical framework for modeling open systems is introduced, based on a four-dimensional manifold with a structural axis of equilibrium L and the phenomenon–time law. In this framework, the conserved quantities are not simply described by spatiotemporal coordinates, but their evolution path, input flow, and equilibrium state are represented explicitly along the L-axis. Thus, the conservation law is applied directly to the geometry of the system state space, not as an external constraint. The proposed framework separates the dynamics of open systems into three general components: initial irreversible acceptance, two-way equilibrium acceptance, and residual phenomena. The geometric-physical coordinate framework introduces an analytical tool for the geometric representation and structural comparison of the behavior of open systems under known non-equilibrium thermodynamics. Unlike conventional empirical approaches, the present framework allows for the analytical determination of capacities, equilibrium thresholds, and limit behaviors of the system without heavy reliance on experimental calibration. The results show that the phenomenon-time law can be used as a unified geometric foundation for modeling open systems under survival laws and provides a coherent platform for theoretical analysis, dynamic simulation, and interdisciplinary generalization.

Published in	Science Discovery Physics (Volume 1, Issue 1)
DOI	10.11648/j.sdp.20260101.15
Page(s)	51-61
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Open Systems, Phenomenon-Time Law, Input-Output Balance, Irreversibility, System Capacity

References

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Shamohammadi, S. (2026). Geometric-Physical Coordinate Framework of Phenomena-Time in Open Systems with L-Balance Axis Constraint. Science Discovery Physics, 1(1), 51-61. https://doi.org/10.11648/j.sdp.20260101.15

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Shamohammadi, S. Geometric-Physical Coordinate Framework of Phenomena-Time in Open Systems with L-Balance Axis Constraint. Sci. Discov. Phys. 2026, 1(1), 51-61. doi: 10.11648/j.sdp.20260101.15

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Shamohammadi S. Geometric-Physical Coordinate Framework of Phenomena-Time in Open Systems with L-Balance Axis Constraint. Sci Discov Phys. 2026;1(1):51-61. doi: 10.11648/j.sdp.20260101.15

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@article{10.11648/j.sdp.20260101.15,
  author = {Shayan Shamohammadi},
  title = {Geometric-Physical Coordinate Framework of Phenomena-Time in Open Systems with L-Balance Axis Constraint},
  journal = {Science Discovery Physics},
  volume = {1},
  number = {1},
  pages = {51-61},
  doi = {10.11648/j.sdp.20260101.15},
  url = {https://doi.org/10.11648/j.sdp.20260101.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sdp.20260101.15},
  abstract = {Mathematical models used in hydrology, physics, chemistry, and many engineering systems are largely based on empirical or semi-empirical relationships. One fundamental reason for this is that classical coordinate systems—whether Cartesian or relativistic spacetime—are inherently incapable of representing the laws of conservation in open systems. These frameworks describe the instantaneous state of quantities, but do not inherently incorporate the flow, input–output balance, and irreversible nature of processes into their geometric structure. In this paper, a new geometric–physical framework for modeling open systems is introduced, based on a four-dimensional manifold with a structural axis of equilibrium L and the phenomenon–time law. In this framework, the conserved quantities are not simply described by spatiotemporal coordinates, but their evolution path, input flow, and equilibrium state are represented explicitly along the L-axis. Thus, the conservation law is applied directly to the geometry of the system state space, not as an external constraint. The proposed framework separates the dynamics of open systems into three general components: initial irreversible acceptance, two-way equilibrium acceptance, and residual phenomena. The geometric-physical coordinate framework introduces an analytical tool for the geometric representation and structural comparison of the behavior of open systems under known non-equilibrium thermodynamics. Unlike conventional empirical approaches, the present framework allows for the analytical determination of capacities, equilibrium thresholds, and limit behaviors of the system without heavy reliance on experimental calibration. The results show that the phenomenon-time law can be used as a unified geometric foundation for modeling open systems under survival laws and provides a coherent platform for theoretical analysis, dynamic simulation, and interdisciplinary generalization.},
 year = {2026}
}

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TY  - JOUR
T1  - Geometric-Physical Coordinate Framework of Phenomena-Time in Open Systems with L-Balance Axis Constraint
AU  - Shayan Shamohammadi
Y1  - 2026/02/25
PY  - 2026
N1  - https://doi.org/10.11648/j.sdp.20260101.15
DO  - 10.11648/j.sdp.20260101.15
T2  - Science Discovery Physics
JF  - Science Discovery Physics
JO  - Science Discovery Physics
SP  - 51
EP  - 61
PB  - Science Publishing Group
UR  - https://doi.org/10.11648/j.sdp.20260101.15
AB  - Mathematical models used in hydrology, physics, chemistry, and many engineering systems are largely based on empirical or semi-empirical relationships. One fundamental reason for this is that classical coordinate systems—whether Cartesian or relativistic spacetime—are inherently incapable of representing the laws of conservation in open systems. These frameworks describe the instantaneous state of quantities, but do not inherently incorporate the flow, input–output balance, and irreversible nature of processes into their geometric structure. In this paper, a new geometric–physical framework for modeling open systems is introduced, based on a four-dimensional manifold with a structural axis of equilibrium L and the phenomenon–time law. In this framework, the conserved quantities are not simply described by spatiotemporal coordinates, but their evolution path, input flow, and equilibrium state are represented explicitly along the L-axis. Thus, the conservation law is applied directly to the geometry of the system state space, not as an external constraint. The proposed framework separates the dynamics of open systems into three general components: initial irreversible acceptance, two-way equilibrium acceptance, and residual phenomena. The geometric-physical coordinate framework introduces an analytical tool for the geometric representation and structural comparison of the behavior of open systems under known non-equilibrium thermodynamics. Unlike conventional empirical approaches, the present framework allows for the analytical determination of capacities, equilibrium thresholds, and limit behaviors of the system without heavy reliance on experimental calibration. The results show that the phenomenon-time law can be used as a unified geometric foundation for modeling open systems under survival laws and provides a coherent platform for theoretical analysis, dynamic simulation, and interdisciplinary generalization.
VL  - 1
IS  - 1
ER  -

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Shayan Shamohammadi

Department of Water Engineering, Shahrekord University, Shahrekord, Iran

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Shamohammadi, S. (2026). Geometric-Physical Coordinate Framework of Phenomena-Time in Open Systems with L-Balance Axis Constraint. Science Discovery Physics, 1(1), 51-61. https://doi.org/10.11648/j.sdp.20260101.15

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Shamohammadi, S. Geometric-Physical Coordinate Framework of Phenomena-Time in Open Systems with L-Balance Axis Constraint. Sci. Discov. Phys. 2026, 1(1), 51-61. doi: 10.11648/j.sdp.20260101.15

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AMA Style

Shamohammadi S. Geometric-Physical Coordinate Framework of Phenomena-Time in Open Systems with L-Balance Axis Constraint. Sci Discov Phys. 2026;1(1):51-61. doi: 10.11648/j.sdp.20260101.15

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@article{10.11648/j.sdp.20260101.15,
  author = {Shayan Shamohammadi},
  title = {Geometric-Physical Coordinate Framework of Phenomena-Time in Open Systems with L-Balance Axis Constraint},
  journal = {Science Discovery Physics},
  volume = {1},
  number = {1},
  pages = {51-61},
  doi = {10.11648/j.sdp.20260101.15},
  url = {https://doi.org/10.11648/j.sdp.20260101.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sdp.20260101.15},
  abstract = {Mathematical models used in hydrology, physics, chemistry, and many engineering systems are largely based on empirical or semi-empirical relationships. One fundamental reason for this is that classical coordinate systems—whether Cartesian or relativistic spacetime—are inherently incapable of representing the laws of conservation in open systems. These frameworks describe the instantaneous state of quantities, but do not inherently incorporate the flow, input–output balance, and irreversible nature of processes into their geometric structure. In this paper, a new geometric–physical framework for modeling open systems is introduced, based on a four-dimensional manifold with a structural axis of equilibrium L and the phenomenon–time law. In this framework, the conserved quantities are not simply described by spatiotemporal coordinates, but their evolution path, input flow, and equilibrium state are represented explicitly along the L-axis. Thus, the conservation law is applied directly to the geometry of the system state space, not as an external constraint. The proposed framework separates the dynamics of open systems into three general components: initial irreversible acceptance, two-way equilibrium acceptance, and residual phenomena. The geometric-physical coordinate framework introduces an analytical tool for the geometric representation and structural comparison of the behavior of open systems under known non-equilibrium thermodynamics. Unlike conventional empirical approaches, the present framework allows for the analytical determination of capacities, equilibrium thresholds, and limit behaviors of the system without heavy reliance on experimental calibration. The results show that the phenomenon-time law can be used as a unified geometric foundation for modeling open systems under survival laws and provides a coherent platform for theoretical analysis, dynamic simulation, and interdisciplinary generalization.},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Geometric-Physical Coordinate Framework of Phenomena-Time in Open Systems with L-Balance Axis Constraint
AU  - Shayan Shamohammadi
Y1  - 2026/02/25
PY  - 2026
N1  - https://doi.org/10.11648/j.sdp.20260101.15
DO  - 10.11648/j.sdp.20260101.15
T2  - Science Discovery Physics
JF  - Science Discovery Physics
JO  - Science Discovery Physics
SP  - 51
EP  - 61
PB  - Science Publishing Group
UR  - https://doi.org/10.11648/j.sdp.20260101.15
AB  - Mathematical models used in hydrology, physics, chemistry, and many engineering systems are largely based on empirical or semi-empirical relationships. One fundamental reason for this is that classical coordinate systems—whether Cartesian or relativistic spacetime—are inherently incapable of representing the laws of conservation in open systems. These frameworks describe the instantaneous state of quantities, but do not inherently incorporate the flow, input–output balance, and irreversible nature of processes into their geometric structure. In this paper, a new geometric–physical framework for modeling open systems is introduced, based on a four-dimensional manifold with a structural axis of equilibrium L and the phenomenon–time law. In this framework, the conserved quantities are not simply described by spatiotemporal coordinates, but their evolution path, input flow, and equilibrium state are represented explicitly along the L-axis. Thus, the conservation law is applied directly to the geometry of the system state space, not as an external constraint. The proposed framework separates the dynamics of open systems into three general components: initial irreversible acceptance, two-way equilibrium acceptance, and residual phenomena. The geometric-physical coordinate framework introduces an analytical tool for the geometric representation and structural comparison of the behavior of open systems under known non-equilibrium thermodynamics. Unlike conventional empirical approaches, the present framework allows for the analytical determination of capacities, equilibrium thresholds, and limit behaviors of the system without heavy reliance on experimental calibration. The results show that the phenomenon-time law can be used as a unified geometric foundation for modeling open systems under survival laws and provides a coherent platform for theoretical analysis, dynamic simulation, and interdisciplinary generalization.
VL  - 1
IS  - 1
ER  -

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