Related papers: Fixed point theorems on partial randomness
The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed by our former works [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008] and [K. Tadaki, Proceedings of…
We develop a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities, such as free energy, energy, statistical mechanical entropy, and specific heat, into algorithmic…
The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed in our former work [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008], where we introduced the notion of…
Algorithmic entropy can be seen as a special case of entropy as studied in statistical mechanics. This viewpoint allows us to apply many techniques developed for use in thermodynamics to the subject of algorithmic information theory. In…
An attempt toward the operational formulation of quantum thermodynamics is made by employing the recently proposed operations forming positive operator-valued measures for generating thermodynamic processes. The quantity of heat as well as…
In this paper, we investigate the computability of thermodynamic invariants at zero temperature for one-dimensional subshifts of finite type. In particular, we prove that the residual entropy (i.e., the joint ground state entropy) is an…
We present a relativistic quantum mechanics of a point mass with absolute thermodynamic time and temperature, combined to a single complex parameter of evolution. In this theory, the geometric time is introduced as one of space-time…
Developing a thermodynamic theory of computation is a challenging task at the interface of non-equilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times,…
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper,…
We study the heat statistics of a multi-level $N$-dimensional quantum system monitored by a sequence of projective measurements. The late-time, asymptotic properties of the heat characteristic function are analyzed in the thermodynamic…
We illustrate recent results concerning the validity of the work fluctuation theorem in open quantum systems [M. Campisi, P. Talkner, and P. H\"{a}nggi, Phys. Rev. Lett. {\bf 102}, 210401 (2009)], by applying them to a solvable model of an…
We investigate the theory of thermodynamic formalism from the perspective of computable analysis, with a special focus on the computability of equilibrium states. Specifically, we develop two complementary general approaches to verify the…
In this paper we examine the behavior in temperature of the free energy on quantum systems in an arbitrary number of dimensions. We define from the free energy a function $C$ of the coupling constants and the temperature, which in the…
The significance of statistical physics concepts such as entropy extends far beyond classical thermodynamics. We interpret the similarity between partitions in statistical mechanics and partitions in Bayesian inference as an articulation of…
Do negative absolute temperatures matter physics and specifically Statistical Physics? We provide evidence that we can certainly answer positively to this vexata quaestio. The great majority of models investigated by statistical mechanics…
We develop a physics-based model for classical computation based on autonomous quantum thermal machines. These machines consist of few interacting quantum bits (qubits) connected to several environments at different temperatures. Heat flows…
Thermodynamics relies on the possibility to describe systems composed of a large number of constituents in terms of few macroscopic variables. Its foundations are rooted into the paradigm of statistical mechanics, where thermal properties…
Stochastic thermodynamics is formulated under the assumption of perfect knowledge of all thermodynamic parameters. However, in any real-world experiment, there is non-zero uncertainty about the precise value of temperatures, chemical…
Thermodynamic random processes in thermal systems are generally associated with one or several relaxation times, the inverse of which are formally homogeneous with energy. Here, we show in a precise way that the periodic modification of…
Heat, work and entropy production: the statistical distribution of such quantities are constrained by the fluctuation theorems (FT), which reveal crucial properties about the nature of non-equilibrium dynamics. In this paper we report…