Related papers: Chaitin's Omega and an Algorithmic Phase Transitio…
In our former work [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008], we developed a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities at temperature T,…
This paper studies a Large Language Model's ability to exhibit intelligence equivalent to that of a human by analyzing temperature-induced phase transitions, abrupt changes in the macroscopic behavior of a system, in the Turing test. We…
We analyze the phase structure of $SU(\infty)$ gauge theory at finite temperature using matrix models. Our basic assumption is that the effective potential is dominated by double-trace terms for the Polyakov loops. As a function of the…
Quantization of energy is a quintessential characteristic of quantum systems. Here we analyze its effects on the operation of Otto cycle heat machines and show that energy quantization alone may alter and increase machine performance in…
An instantaneous temperature path of a point particle in the space - temperature manifold can be represented as a string of length L=1/kT (thermostring). The thermostring swepts a surface in the space-time-temperature manyfold at its…
Heat engines usually operate by exchanging heat with thermal baths at different (positive) temperatures. Nonthermal baths may, however, lead to a significant performance boost. We here experimentally analyze the power output of a…
Foundations of the theory of quantum Turing machines are investigated. The protocol for the preparation and the measurement of quantum Turing machines is discussed. The local transition functions are characterized for fully general quantum…
In this Letter, we numerically present the possibility of the first-order phase transition occurring through the thermal fluctuation in the early universe. We find that when the temperature is slightly higher than the mass scale of the…
The aim of this paper is to undertake an experimental investigation of the trade-offs between program-size and time computational complexity. The investigation includes an exhaustive exploration and systematic study of the functions…
The concept of majorisation is explored as a tool to characterize the performance of a quantum Otto engine in the quasi-static regime. For a working substance in the form of a spin of arbitrary magnitude, majorisation yields a necessary and…
We present a novel mechanism for the anomalous behaviour of the specific heat in low-temperature amorphous solids. The analytic solution of a mean-field model belonging to the same universality class as high-dimensional glasses, the…
The state space of a generic string bit model is spanned by $N\times N$ matrix creation operators acting on a vacuum state. Such creation operators transform in the adjoint representation of the color group $U(N)$ (or $SU(N)$ if the…
Experimentally there exist many materials with first-order phase transitions at finite temperature that display quantum criticality. Classically, a strain-energy density coupling is known to drive first-order transitions in compressible…
We compute the transition temperature $T_c$ and the Ginzburg temperature $T_{\rm G}$ above $T_c$ near a quantum critical point at the boundary of an ordered phase with a broken discrete symmetry in a two-dimensional metallic electron…
To reveal the role of the quantumness in the Otto cycle and to discuss the validity of the thermodynamic uncertainty relation (TUR) in the cycle, we study the quantum Otto cycle and its classical counterpart. In particular, we calculate…
The third law of thermodynamics, also known as the Nernst unattainability principle, puts a fundamental bound on how close a system, whether classical or quantum, can be cooled to a temperature near to absolute zero. On the other hand, a…
We formalize and prove the extension to finite temperature of a class of quantum phase transitions, acting as condensations in the space of states, recently introduced and discussed at zero temperature~(Ostilli and Presilla 2021 \textit{J.…
All ensembles of statistical mechanics are equivalent in the sense that they give the equivalent thermodynamic functions in the thermodynamic limit. However, when investigating microscopic structures in the first-order phase transition…
We find that the high temperature limit of the free energy per unit length for the rigid string agrees dimensionally with that of the QCD string (unlike the Nambu-Goto string). The sign, and in fact the phase, do not agree. While this may…
We investigate a quantum Otto engine with a quantum Ising spin glass as the working medium to explore the scaling behavior of work output and thermodynamic performance concerning system size, particularly near the critical point.…