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Being able to measure time, whether directly or indirectly, is a significant advantage for an organism. It allows for the timely reaction to regular or predicted events, reducing the pressure for fast processing of sensory input. Thus,…
We develop an abstract model of atomic clocks that fully describes the dynamics of repeated synchronization between a classical oscillator and a quantum reference. We prove existence of a stationary state of the model and study its…
A fundamental description of time can be consistent not only with the usual monotonic behavior but also with a periodic physical clock variable, coupled to the degrees of freedom of a system evolving in time. Generically, one would in fact…
All clocks, classical or quantum, are open non equilibrium irreversible systems subject to the constraints of thermodynamics. Using examples I show that these constraints necessarily limit the performance of clocks and that good clocks…
The dynamics of an unique type of clock mechanism known as grasshopper escapement is investigated with the aim of evaluating its accuracy in a noisy environment. It is demonstrated that the clock's precision scales linearly with the rate of…
In the last ten years extraordinary results in time and frequency metrology have been demonstrated. Frequency-stabilization techniques for continuous-wave lasers and femto-second optical frequency combs have enabled a rapid development of…
Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract…
According to thermodynamics, the inevitable increase of entropy allows the past to be distinguished from the future. From this perspective, any clock must incorporate an irreversible process that allows this flow of entropy to be tracked.…
One of the characteristic features of categorical systems theory is that the behavior of systems can be characterized by certain morphisms into them. In other words, behaviors form a representable covariant functor to Set. And more…
Animals exploit time to survive in the world. Temporal information is required for higher-level cognitive abilities such as planning, decision making, communication, and effective cooperation. Since time is an inseparable part of cognition,…
The Thermal Time Hypotheis (TTH) has been proposed as a general method for identifying a time variable from within background-free theories which do not come equipped with a pre-defined clock variable. Here, we explore some implications of…
A driven linear oscillator and a feedback mechanism are two necessary elements of any classical periodic clock. Here, we introduce a novel, fully quantum clock using a driven oscillator in the quantum regime and coherent quantum feedback.…
Arguments are given that time must be defined in an operative manner,i.e., by constructing devices which can serve as clocks.The investigation of such devices leads to the conclusion that there is a principal uncertainity of time if one…
Time plays a crucial role in the intuitive understanding of the world around us. Within quantum mechanics, however, time is not usually treated as an observable quantity; it enters merely as a parameter in the laws of motion of physical…
In this paper I discuss the concept of time in physics. I consider the thermal time hypothesis and I claim that thermal clocks and atomic clocks measure different physical times, whereby thermal time and relativistic time are not compatible…
The thermodynamic uncertainty relation expresses a seemingly universal trade-off between the cost for driving an autonomous system and precision in any output observable. It has so far been proven for discrete systems and for overdamped…
The origin and nature of time in complex systems is explored using quantum (or 'Feynman') clocks and the signals produced by them. Networks of these clocks provide the basis for the evolution of complex systems. The general concept of…
The exquisite control exhibited over quantum states of individual particles has revolutionized the field of precision measurement, as exemplified by the most accurate atomic clock realized in single trapped ions. Whereas many-atom lattice…
Brownian clocks are biomolecular networks that can count time. A paradigmatic example are proteins that go through a cycle thus regulating some oscillatory behaviour in a living system. Typically, such a cycle requires free energy often…
We present a new framework to study the time variation of fundamental constants in a model-independent way. Model independence implies more free parameters than assumed in previous studies. Using data from atomic clocks based on $^{87}$Sr,…