Effective Thermodynamics of a Volume-Dependent Qubit
Abstract
We develop an effective thermodynamics for a qubit whose energy gap depends inversely on a volume-like control parameter, Δ(V)=Δ0/V, where V is a spectral-control coordinate rather than a literal mechanical volume. Starting from the canonical Gibbs state, we derive a complete thermodynamic structure from the Helmholtz potential and its Legendre and stability properties, including the fundamental relation S(U,V), a generalized pressure conjugate to V, the equation of state U=PV, the first law, and the associated Maxwell relations. Reversible adiabats preserve the Gibbs populations and satisfy TV=const. and PV2=const., corresponding to an effective exponent γ=2. The resulting effective Carnot cycle attains the Carnot efficiency, ηCarnot=1−TC/TH, whereas the Otto cycle yields ηOtto=1−Vmin/Vmax and remains strictly sub-Carnot at finite work output. We identify the source of Otto irreversibility exactly: entropy is produced entirely during the isochoric thermalizations, and the cycle entropy production quantifies the informational mismatch between the adiabatically transported states and the reservoir-selected Gibbs states through the sum of the corresponding quantum relative entropies. Finally, we show that unitary-generated nonpassivity can act as a nonequilibrium battery, producing an apparent efficiency above Carnot when its preparation cost is omitted. At the same time, complete work accounting restores the thermodynamic bound.
Related
- Nonequilibrium Apparent-Horizon Thermodynamics in Effective Loop Quantum Cosmology
- 𝒩=2 supersymmetric Yang-Mills thermodynamics from effective field theory
- Quantum memory in an effective Λ-type system using dynamic detuning control of a superconducting qubit pair
- Black hole thermodynamics and KK photon quantum corrections in 2D effective dilaton gravity
- Thermodynamics in symmetry-improved Cornwall-Jackiw-Tomboulis formalism: application to the low-energy effective theory of QCD
BibTeX
@misc{cesario2026effective,
title = {{Effective Thermodynamics of a Volume-Dependent Qubit}},
author = {André T. Cesário and Marcela Herrera},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08040},
eprint = {2611.08040},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08040},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Effective Thermodynamics of a Volume-Dependent Qubit
AU - André T. Cesário
AU - Marcela Herrera
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08040
UR - https://arxiv.org/abs/2611.08040
AB - We develop an effective thermodynamics for a qubit whose energy gap depends inversely on a volume-like control parameter, Δ(V)=Δ_0/V, where V is a spectral-control coordinate rather than a literal mechanical volume. Starting from the canonical Gibbs state, we derive a complete thermodynamic structure from the Helmholtz potential and its Legendre and stability properties, including the fundamental relation S(U,V), a generalized pressure conjugate to V, the equation of state U=PV, the first law, and the associated Maxwell relations. Reversible adiabats preserve the Gibbs populations and satisfy TV=const. and PV^2=const., corresponding to an effective exponent γ=2. The resulting effective Carnot cycle attains the Carnot efficiency, η_Carnot=1−T_C/T_H, whereas the Otto cycle yields η_Otto=1−V_min/V_max and remains strictly sub-Carnot at finite work output. We identify the source of Otto irreversibility exactly: entropy is produced entirely during the isochoric thermalizations, and the cycle entropy production quantifies the informational mismatch between the adiabatically transported states and the reservoir-selected Gibbs states through the sum of the corresponding quantum relative entropies. Finally, we show that unitary-generated nonpassivity can act as a nonequilibrium battery, producing an apparent efficiency above Carnot when its preparation cost is omitted. At the same time, complete work accounting restores the thermodynamic bound.
ER -