Lower bounds on fluctuations of thermodynamic currents depend on the nature of time, discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master equations. We prove that current fluctuations in the master equations are always more likely, due to random timings of transitions. This comparison leads to a mapping of the moments of a current between discrete and continuous time. We exploit this mapping to obtain uncertainty bounds. Our results reduce the quests for uncertainty bounds in discrete and continuous time to a single problem.

Is it possible to operate a computing device with zero energy expenditure? This question, once considered just an academic dilemma, has recently become strategic for the future of information and communication technology. In fact, in the last forty years the semiconductor industry has been driven by its ability to scale down the size of the complementary metal-oxide semiconductor-field-effect transistor, the building block of present computing devices, and to increase computing capability density up to a point where the power dissipated in heat during computation has become a serious limitation. To overcome such a limitation, since 2004 the Nanoelectronics Research Initiative has launched a grand challenge to address the fundamental limits of the physics of switches. In Europe, the European Commission has recently funded a set of projects with the aim of minimizing the energy consumption of computing. In this article we briefly review state-of-the-art zero-power computing, with special attention paid to the aspects of energy dissipation at the micro- and nanoscales.

No abstract

In its most conservative formulation, the Landauer principle states that at least of heat must be produced to reset one bit. Theoretical derivations of this result for practical systems require complex mathematical tools; additionally, real experiments are sophisticated and sensitive. In the literature, it's then common practice to look for a global heat production of without further concern for heat exchanges at intermediate times. In this paper we want to recover such kind of description: we take a Brownian particle that moves in a bistable potential as bit. We then consider a reset protocol with a net heat production of and study the time evolution of internal energy, work and heat. In particular, we show that these quantities are fully characterized by the changes that the protocol induces over the wells of the bistable potential.

-Landauer principle describes the minimum heat produced by an informationprocessing device. Recently a new term has been included in the minimum heat production: it's called conditional entropy and takes into account the microstates content of a given logic state. Usually this term is assumed zero in bistable symmetric systems thanks to the strong hypothesis used to derive Landauer principle. In this paper we show that conditional entropy can be nonzero even for bistable symmetric systems and that it can be expressed as the sum of three different terms related to the probabilistic features of the device. The contribution of the three terms to conditional entropy (and thus to minimum heat production) is then discussed for the case of bit-reset.