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About the dissipative Newton equation

Peter Ván

Abstract

The thermodynamic basis of classical mechanics is presented. In this framework, ideal Newtonian mechanics emerges as the zero-dissipation limit of a more general, dissipative theory. The thermodynamic approach predicts a novel dissipative contribution to the momentum that depends on the applied force, leading to a damping coefficient with a specific, experimentally testable dependence on the inertial mass and the spring constant. A torsion balance experiment with variable moment of inertia has been designed to measure this effect. Several known equations, including a thermodynamic version of the Eliezer-Ford-O'Connell equation of radiation reaction, are recovered as special cases.

About the dissipative Newton equation

Abstract

The thermodynamic basis of classical mechanics is presented. In this framework, ideal Newtonian mechanics emerges as the zero-dissipation limit of a more general, dissipative theory. The thermodynamic approach predicts a novel dissipative contribution to the momentum that depends on the applied force, leading to a damping coefficient with a specific, experimentally testable dependence on the inertial mass and the spring constant. A torsion balance experiment with variable moment of inertia has been designed to measure this effect. Several known equations, including a thermodynamic version of the Eliezer-Ford-O'Connell equation of radiation reaction, are recovered as special cases.
Paper Structure (17 sections, 33 equations, 2 figures)

This paper contains 17 sections, 33 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The logic of mechanics and thermodynamics
  3. Thermo-Dynamics of two variables
  4. Example of conservative mechanics
  5. Dissipation and Hamiltonian mechanics
  6. Conservative-like dissipative mechanics
  7. Special cases: the role of force
  8. Newtonian mechanics: $l_1 = 0$ and $l_2 = 0$
  9. Damped mechanics: $l_1 = 0$
  10. Eliezer-Ford-O'Connell-Verhás equation: $l_2 = 0$
  11. Aristotelian resonance: $l=k$
  12. Dissipative momentum: experimental prediction
  13. Discussion
  14. Micro-macro relation of dissipation
  15. Outlook
  16. ...and 2 more sections

Figures (2)

  • Figure 1: The arm of the torsion balance. The upper part at the centre is related to the optical readout. The wires ensure the parallel movability of the masses. When operational, it is suspended upside-down.
  • Figure 2: The torsion balance with variable moment of inertia in its vacuum chamber. Below is the electronic control unit.