Promoting Fluctuation Theorems into Covariant Forms

Abstract

The principle of covariance, a cornerstone of modern physics, asserts the equivalence of all inertial frames of reference. Fluctuation theorems, as extensions of the second law of thermodynamics, establish universal connections between irreversibility and fluctuation in terms of stochastic thermodynamic quantities. However, these relations typically assume that both the thermodynamic system and the heat bath are at rest with respect to the observer, thereby failing to satisfy the principle of covariance. In this study, by introducing covariant work and heat that incorporate both energy-related and momentum-related components, we promote fluctuation theorems into covariant forms applicable to moving thermodynamic systems and moving heat baths. We illustrate this framework with two examples: the work statistics of a relativistic stochastic field and the heat statistics of a relativistic Brownian motion. Although our study is carried out in the context of special relativity, the results can be extended to the nonrelativistic limit. Our work combines the principle of covariance and fluctuation theorems into a coherent framework and may have applications in the study of thermodynamics relevant to cosmic microwave background as well as the radiative heat transfer and noncontact friction between relatively moving bodies.

References in corpus (29)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Classical and Quantum Fluctuation Theorems for Heat Exchange
• Relativistic Brownian Motion
• Planck 2013 results. XXVII. Doppler boosting of the CMB: Eppur si muove
• Theory of the interaction forces and the heat transfer between moving bodies mediated by the fluctuating electromagnetic field
• Theory of Relativistic Brownian Motion: The (1+3)-Dimensional Case
• The Reality of Casimir Friction
• Fluctuation dynamics in a relativistic fluid with a critical point
• Three Views of a Secret in Relativistic Thermodynamics
• Work distributions on quantum fields
• Jarzynski Equality for Driven Quantum Field Theories
• A field-theoretic approach to nonequilibrium work identities
• Inverse Temperature 4-vector in Special Relativity
• Stochastic thermodynamics of relativistic Brownian motion
• Lorentz Transform of Black Body Radiation Temperature
• Quantum work distributions associated with the dynamical Casimir effect
• The First Law of Quantum Field Thermodynamics
• Fluctuating Relativistic hydrodynamics from Crooks theorem
• Relativistic Fluctuation Theorems: Theory and explicit examples
• Lorentz Transformation of Blackbody Radiation
• Relativistic stochastic mechanics I: Langevin equation from observer's perspective
• Fluctuation theorem for entropy production during effusion of a relativistic ideal gas
• Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs
• Relativistic stochastic mechanics II: Reduced Fokker-Planck equation in curved spacetime
• The Relativistic Blackbody Spectrum in Inertial and Non-Inertial Reference Frames
• General relativistic stochastic thermodynamics
• Exact Work Distribution and Jarzynski's Equality of a Relativistic Particle in an Expanding Piston

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