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Nonholonomic constraints at finite temperature.

Eduardo A Jagla1, Anthony M Bloch2, Alberto G Rojo3

  • 1UNCUYO, CONICET, CNEA, Comisión Nacional de Energía Atómica, Instituto Balseiro, Centro Atómico Bariloche, Av. Bustillo 9500 (R8402AGP) Bariloche, Río Negro, Argentina.

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Dynamical systems with nonholonomic constraints coupled to a thermal bath can violate the second law of thermodynamics. Physically implementing constraints resolves this paradox, showing limits on idealized nonholonomic systems.

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Area of Science:

  • Physics
  • Thermodynamics
  • Statistical Mechanics

Background:

  • Nonholonomic constraints in dynamical systems present unique challenges.
  • Coupling these systems to a thermal bath introduces thermodynamic considerations.
  • The Chaplygin sleigh is a canonical model for studying nonholonomic dynamics.

Purpose of the Study:

  • To investigate the thermodynamic behavior of nonholonomic dynamical systems coupled to a thermal bath.
  • To resolve the apparent violation of the second law of thermodynamics predicted by naive Langevin approaches.
  • To establish fundamental limits on the physical realization of idealized nonholonomic constraints.

Main Methods:

  • A straightforward Langevin-type approach was initially employed.
  • The nonholonomic constraint was implemented as a limiting case of viscous interaction.
  • Stochastic forces, consistent with fluctuation-dissipation relations, were incorporated at finite temperatures.

Main Results:

  • A naive Langevin approach predicted work extraction, violating the second law of thermodynamics.
  • Physically motivated implementation of constraints, including stochastic forces, restored thermodynamic compliance.
  • The study demonstrates that idealized nonholonomic constraints have fundamental physical realizability limits.

Conclusions:

  • Naive modeling of nonholonomic systems in thermal baths can lead to thermodynamic paradoxes.
  • A physically grounded approach, incorporating fluctuation-dissipation relations, is crucial for accurate modeling.
  • The findings highlight inherent limitations in the practical implementation of idealized nonholonomic constraints.