Thermodynamic Entropy as a Noether Invariant

Abstract:We elaborate on existing notions of contact geometry and Poisson geometry as applied to the classical ideal gas. Specifically, we observe that it is possible to describe its dynamics using a 3-dimensional contact submanifold of the standard 5-dimensional contact manifold used in the literature. This reflects the fact that the internal energy of the ideal gas depends exclusively on its temperature. We also present a Poisson algebra of thermodynamic operators for a quantum-like description of the classical ideal gas. The central element of this Poisson algebra is proportional to Boltzmann's constant. A Hilbert space of states is identified and a system of wave equations governing the wavefunction is found. Expectation values for the operators representing pressure, volume and temperature are found to satisfy the classical equations of state.

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“…A model containing both Planck's constanth and Boltzmann's constant k B has been considered in ref. [24].…”

Section: Discussionmentioning

confidence: 99%

On the Contact Geometry and the Poisson Geometry of the Ideal Gas

Isidro

Córdoba

2018

Entropy

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“…which means that the overlap between P E j ,hj j∆t and each eigenstate in the shell is equally weighted up to the sub-exponential factor in N . Thus, (36) becomes…”

Section: B Evaluation Of Bjmentioning

confidence: 99%

Thermodynamical path integral and emergent symmetry

2019

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We investigate a thermally isolated quantum many-body system with an external control represented by a step protocol of a parameter. The propagator at each step of the parameter change is described by thermodynamic quantities under some assumptions. For the time evolution of such systems, we formulate a path integral over the trajectories in the thermodynamic state space. In particular, for quasi-static operations, we derive an effective action of the thermodynamic entropy and its canonically conjugate variable. Then, the symmetry for the uniform translation of the conjugate variable emerges in the path integral. This leads to the entropy as a Noether invariant in quantum mechanics.

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“…In recent years several proposals were made to identify a symmetry which generates a conserved entropy current in the absence of dissipation, see e.g. [6][7][8][9][10]. More recently, the authors of [11,12] have maintained that a positive divergence entropy current can be constructed by appealing to a positivity constraint on the imaginary part of the Schwinger-Keldysh effective action.…”

Section: Contents 1 Introductionmentioning

confidence: 99%

An entropy current in superspace

Jensen

Marjieh

Pinzani-Fokeeva

et al. 2019

J. High Energ. Phys.

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We construct an entropy current using a supersymmetric formulation of the low-energy effective action for the Schwinger-Keldysh generating functional. We define an entropy current quantum mechanically by coupling it to an external source. It is given by the bottom component of an entropy current superfield which is conserved in superspace, but when restricted to real space satisfies a non-conservation law. Our analysis is valid in the probe limit which allows us to fully treat quantum fluctuations.

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Thermodynamic Entropy as a Noether Invariant

Cited by 33 publications

References 37 publications

On the Contact Geometry and the Poisson Geometry of the Ideal Gas

On the Contact Geometry and the Poisson Geometry of the Ideal Gas

Thermodynamical path integral and emergent symmetry

An entropy current in superspace

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